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  <link:labelLink xlink:role="http://www.xbrl.org/2003/role/link" xlink:type="extended">
    <link:label id="lab_us-gaap_ProceedsFromLongTermLinesOfCredit_b905f765-46e8-4376-b071-c4db09e72103_verboseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromLongTermLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from the issuance of debt</link:label>
    <link:label id="lab_us-gaap_ProceedsFromLongTermLinesOfCredit_4273affd-90d1-4c41-90bb-c224699d9f37_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromLongTermLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from lines of credit</link:label>
    <link:label id="lab_us-gaap_ProceedsFromLongTermLinesOfCredit_label_en-US" xlink:label="lab_us-gaap_ProceedsFromLongTermLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Long-Term Lines of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromLongTermLinesOfCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ProceedsFromLongTermLinesOfCredit"/>
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    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_a3157690-21ca-4aa0-b186-d856fd8c4b0e_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustments to reconcile net loss to net cash used in operating activities:</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustments to Reconcile Net Income (Loss) to Cash Provided by (Used in) Operating Activities [Abstract]</link:label>
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    <link:label id="lab_srt_RangeMember_5dcb6407-d5d7-4b60-800c-0dd39e0a2187_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_RangeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeMember" xlink:to="lab_srt_RangeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInPrepaidExpense_af617a03-a18b-459f-aca1-1b036967142c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInPrepaidExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Prepaid expenses</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInPrepaidExpense_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInPrepaidExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Prepaid Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInPrepaidExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncreaseDecreaseInPrepaidExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInPrepaidExpense" xlink:to="lab_us-gaap_IncreaseDecreaseInPrepaidExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdTradingDays_a887ec04-f37b-4630-b773-29fe704612a2_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdTradingDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of warrant or right, conversion terms, threshold trading days</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdTradingDays_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdTradingDays" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Conversion Terms, Threshold Trading Days</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdTradingDays_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdTradingDays" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Conversion Terms, Threshold Trading Days</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightConversionTermsThresholdTradingDays" xlink:href="tlsi-20250331.xsd#tlsi_ClassOfWarrantOrRightConversionTermsThresholdTradingDays"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightConversionTermsThresholdTradingDays" xlink:to="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdTradingDays" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_LoanFacilityJune302025Member_14950296-c9fa-4d95-a796-21f065877a84_terseLabel_en-US" xlink:label="lab_tlsi_LoanFacilityJune302025Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan Facility, June 30, 2025</link:label>
    <link:label id="lab_tlsi_LoanFacilityJune302025Member_label_en-US" xlink:label="lab_tlsi_LoanFacilityJune302025Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan Facility, June 30, 2025 [Member]</link:label>
    <link:label id="lab_tlsi_LoanFacilityJune302025Member_documentation_en-US" xlink:label="lab_tlsi_LoanFacilityJune302025Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan Facility, June 30, 2025</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_LoanFacilityJune302025Member" xlink:href="tlsi-20250331.xsd#tlsi_LoanFacilityJune302025Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_LoanFacilityJune302025Member" xlink:to="lab_tlsi_LoanFacilityJune302025Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_7e63615e-bede-46f9-a223-0aa29e2d82ca_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Increase (decrease) in cash, cash equivalents and restricted cash</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Period Increase (Decrease), Including Exchange Rate Effect</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DebtInstrumentMinimumVariableRateSOFRFloor_e67fd6a1-06af-491f-8b4c-29cc75577c0c_terseLabel_en-US" xlink:label="lab_tlsi_DebtInstrumentMinimumVariableRateSOFRFloor" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SOFR floor</link:label>
    <link:label id="lab_tlsi_DebtInstrumentMinimumVariableRateSOFRFloor_label_en-US" xlink:label="lab_tlsi_DebtInstrumentMinimumVariableRateSOFRFloor" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Minimum Variable Rate, SOFR Floor</link:label>
    <link:label id="lab_tlsi_DebtInstrumentMinimumVariableRateSOFRFloor_documentation_en-US" xlink:label="lab_tlsi_DebtInstrumentMinimumVariableRateSOFRFloor" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Minimum Variable Rate, SOFR Floor</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DebtInstrumentMinimumVariableRateSOFRFloor" xlink:href="tlsi-20250331.xsd#tlsi_DebtInstrumentMinimumVariableRateSOFRFloor"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DebtInstrumentMinimumVariableRateSOFRFloor" xlink:to="lab_tlsi_DebtInstrumentMinimumVariableRateSOFRFloor" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_28bd7ea7-7a6c-4ae8-8f91-51588be23d71_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other current liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesCurrent" xlink:to="lab_us-gaap_OtherLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_TradingSymbol_030ec1c8-7e46-4418-8d1d-84cddaa28dc4_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:label id="lab_dei_TradingSymbol_label_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_TradingSymbol"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_TradingSymbol" xlink:to="lab_dei_TradingSymbol" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllTradingArrangementsMember_terseLabel_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Trading Arrangements</link:label>
    <link:label id="lab_ecd_AllTradingArrangementsMember_label_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Trading Arrangements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllTradingArrangementsMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AllTradingArrangementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllTradingArrangementsMember" xlink:to="lab_ecd_AllTradingArrangementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_CompActuallyPaidVsNetIncomeTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_LineOfCreditFacilityExitFeePercentage_bb205ca5-35fa-46e6-ba8f-29d007f0f679_terseLabel_en-US" xlink:label="lab_tlsi_LineOfCreditFacilityExitFeePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exit fee percentage</link:label>
    <link:label id="lab_tlsi_LineOfCreditFacilityExitFeePercentage_label_en-US" xlink:label="lab_tlsi_LineOfCreditFacilityExitFeePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line Of Credit Facility, Exit Fee Percentage</link:label>
    <link:label id="lab_tlsi_LineOfCreditFacilityExitFeePercentage_documentation_en-US" xlink:label="lab_tlsi_LineOfCreditFacilityExitFeePercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line Of Credit Facility, Exit Fee Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_LineOfCreditFacilityExitFeePercentage" xlink:href="tlsi-20250331.xsd#tlsi_LineOfCreditFacilityExitFeePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_LineOfCreditFacilityExitFeePercentage" xlink:to="lab_tlsi_LineOfCreditFacilityExitFeePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonNeosMember_terseLabel_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-NEOs</link:label>
    <link:label id="lab_ecd_NonNeosMember_label_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-NEOs [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonNeosMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_NonNeosMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonNeosMember" xlink:to="lab_ecd_NonNeosMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_16773e28-0549-4f9c-99de-8393001d0bac_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based payment arrangement, contractual term</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightWarrantsIssuedDelayedDrawCommitmentAmountPercentage_6b66028a-d536-4ae9-b5c8-1bec4e234275_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightWarrantsIssuedDelayedDrawCommitmentAmountPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants issued, delayed draw commitment amount, percentage</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightWarrantsIssuedDelayedDrawCommitmentAmountPercentage_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightWarrantsIssuedDelayedDrawCommitmentAmountPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Warrants Issued, Delayed Draw Commitment Amount, Percentage</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightWarrantsIssuedDelayedDrawCommitmentAmountPercentage_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightWarrantsIssuedDelayedDrawCommitmentAmountPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Warrants Issued, Delayed Draw Commitment Amount, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightWarrantsIssuedDelayedDrawCommitmentAmountPercentage" xlink:href="tlsi-20250331.xsd#tlsi_ClassOfWarrantOrRightWarrantsIssuedDelayedDrawCommitmentAmountPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightWarrantsIssuedDelayedDrawCommitmentAmountPercentage" xlink:to="lab_tlsi_ClassOfWarrantOrRightWarrantsIssuedDelayedDrawCommitmentAmountPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_NatureOfBusinessLineItems_3f67d307-be41-43f2-9431-a8671a9c93ba_terseLabel_en-US" xlink:label="lab_tlsi_NatureOfBusinessLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nature of Business [Line Items]</link:label>
    <link:label id="lab_tlsi_NatureOfBusinessLineItems_label_en-US" xlink:label="lab_tlsi_NatureOfBusinessLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nature of Business [Line Items]</link:label>
    <link:label id="lab_tlsi_NatureOfBusinessLineItems_documentation_en-US" xlink:label="lab_tlsi_NatureOfBusinessLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Nature of Business [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_NatureOfBusinessLineItems" xlink:href="tlsi-20250331.xsd#tlsi_NatureOfBusinessLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_NatureOfBusinessLineItems" xlink:to="lab_tlsi_NatureOfBusinessLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_Rule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:to="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsEquityInstrumentsIssued_2c117164-d4d1-4218-b26c-ab4f8342826d_terseLabel_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsEquityInstrumentsIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted stock units issued (in shares)</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsEquityInstrumentsIssued_label_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsEquityInstrumentsIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Non-Options Equity Instruments, Issued</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsEquityInstrumentsIssued_documentation_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsEquityInstrumentsIssued" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Non-Options Equity Instruments, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsEquityInstrumentsIssued" xlink:href="tlsi-20250331.xsd#tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsEquityInstrumentsIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsEquityInstrumentsIssued" xlink:to="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsEquityInstrumentsIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AwardsCloseToMnpiDiscTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_30e12d35-a7a0-485f-96ff-91aada6566f0_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_label_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Taxes Paid, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxesPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeTaxesPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxesPaidNet" xlink:to="lab_us-gaap_IncomeTaxesPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_d4c8fe94-3b68-4a0f-85c6-ef3abb0444b4_periodStartLabel_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning Balance</link:label>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_818878e7-5339-40c0-82b7-4273410d0a7d_periodEndLabel_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending Balance</link:label>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_label_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:to="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_RevenueBaseRedemptionLiability_4ee9407b-a1f6-4db8-ba1a-1d881bf1aae2_terseLabel_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue base redemption liability</link:label>
    <link:label id="lab_tlsi_RevenueBaseRedemptionLiability_label_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Liability</link:label>
    <link:label id="lab_tlsi_RevenueBaseRedemptionLiability_documentation_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_RevenueBaseRedemptionLiability" xlink:href="tlsi-20250331.xsd#tlsi_RevenueBaseRedemptionLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_RevenueBaseRedemptionLiability" xlink:to="lab_tlsi_RevenueBaseRedemptionLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_a2d60c82-6618-42d5-887c-02767e0c9344_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock exchange for warrants (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Conversion of Convertible Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ScheduleOfReverseRecapitalizationTable_6b9b3bbe-06a2-4e4d-bb17-ff068bbd5b0a_terseLabel_en-US" xlink:label="lab_tlsi_ScheduleOfReverseRecapitalizationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Reverse Recapitalization [Table]</link:label>
    <link:label id="lab_tlsi_ScheduleOfReverseRecapitalizationTable_label_en-US" xlink:label="lab_tlsi_ScheduleOfReverseRecapitalizationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Reverse Recapitalization [Table]</link:label>
    <link:label id="lab_tlsi_ScheduleOfReverseRecapitalizationTable_documentation_en-US" xlink:label="lab_tlsi_ScheduleOfReverseRecapitalizationTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Reverse Recapitalization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ScheduleOfReverseRecapitalizationTable" xlink:href="tlsi-20250331.xsd#tlsi_ScheduleOfReverseRecapitalizationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ScheduleOfReverseRecapitalizationTable" xlink:to="lab_tlsi_ScheduleOfReverseRecapitalizationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PayVsPerformanceDisclosureLineItems_label_en-US" xlink:label="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PayVsPerformanceDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:to="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockConvertibleConversionPrice_32f04050-d11d-4ee1-8929-ef83384ffec1_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockConvertibleConversionPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, conversion price (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockConvertibleConversionPrice_label_en-US" xlink:label="lab_us-gaap_PreferredStockConvertibleConversionPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Convertible, Conversion Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockConvertibleConversionPrice" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockConvertibleConversionPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockConvertibleConversionPrice" xlink:to="lab_us-gaap_PreferredStockConvertibleConversionPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_AccruedClinicalTrialLiabilityCurrent_442aa8e1-eafd-4776-85d7-802c19ceba40_terseLabel_en-US" xlink:label="lab_tlsi_AccruedClinicalTrialLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued liabilities - clinical trials</link:label>
    <link:label id="lab_tlsi_AccruedClinicalTrialLiabilityCurrent_label_en-US" xlink:label="lab_tlsi_AccruedClinicalTrialLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Clinical Trial Liability, Current</link:label>
    <link:label id="lab_tlsi_AccruedClinicalTrialLiabilityCurrent_documentation_en-US" xlink:label="lab_tlsi_AccruedClinicalTrialLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accrued Clinical Trial Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_AccruedClinicalTrialLiabilityCurrent" xlink:href="tlsi-20250331.xsd#tlsi_AccruedClinicalTrialLiabilityCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_AccruedClinicalTrialLiabilityCurrent" xlink:to="lab_tlsi_AccruedClinicalTrialLiabilityCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PeerGroupTotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:to="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_LoanFacilityInitialCommitmentAmountMember_0bf31935-763d-4ccf-9e1d-8d8d2bd99b9e_terseLabel_en-US" xlink:label="lab_tlsi_LoanFacilityInitialCommitmentAmountMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan Facility, Initial Commitment Amount</link:label>
    <link:label id="lab_tlsi_LoanFacilityInitialCommitmentAmountMember_label_en-US" xlink:label="lab_tlsi_LoanFacilityInitialCommitmentAmountMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan Facility, Initial Commitment Amount [Member]</link:label>
    <link:label id="lab_tlsi_LoanFacilityInitialCommitmentAmountMember_documentation_en-US" xlink:label="lab_tlsi_LoanFacilityInitialCommitmentAmountMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan Facility, Initial Commitment Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_LoanFacilityInitialCommitmentAmountMember" xlink:href="tlsi-20250331.xsd#tlsi_LoanFacilityInitialCommitmentAmountMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_LoanFacilityInitialCommitmentAmountMember" xlink:to="lab_tlsi_LoanFacilityInitialCommitmentAmountMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsReceivable_4b9ccb57-ba09-4fc0-9267-f5492d247167_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsReceivable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accounts Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncreaseDecreaseInAccountsReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:to="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerSharePolicyTextBlock_d7f52e9a-3646-4ecd-88b9-04940271ccab_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Loss per Share</link:label>
    <link:label id="lab_us-gaap_EarningsPerSharePolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerSharePolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EarningsPerSharePolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerSharePolicyTextBlock" xlink:to="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability_b19bfdc2-082b-42ae-851a-9e032ca19848_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Operating Lease Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncreaseDecreaseInOperatingLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryPolicyTextBlock_5ae9684c-3b21-4422-9497-fa2df6c45be2_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Inventory</link:label>
    <link:label id="lab_us-gaap_InventoryPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_InventoryPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InventoryPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryPolicyTextBlock" xlink:to="lab_us-gaap_InventoryPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_NonRule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:to="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PrepaymentPremiumRatePeriodThreeMember_3f9d545a-338d-4e32-bcd9-c9ee5730223e_terseLabel_en-US" xlink:label="lab_tlsi_PrepaymentPremiumRatePeriodThreeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">24 to 36 Months</link:label>
    <link:label id="lab_tlsi_PrepaymentPremiumRatePeriodThreeMember_label_en-US" xlink:label="lab_tlsi_PrepaymentPremiumRatePeriodThreeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepayment Premium Rate, Period Three [Member]</link:label>
    <link:label id="lab_tlsi_PrepaymentPremiumRatePeriodThreeMember_documentation_en-US" xlink:label="lab_tlsi_PrepaymentPremiumRatePeriodThreeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Prepayment Premium Rate, Period Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PrepaymentPremiumRatePeriodThreeMember" xlink:href="tlsi-20250331.xsd#tlsi_PrepaymentPremiumRatePeriodThreeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PrepaymentPremiumRatePeriodThreeMember" xlink:to="lab_tlsi_PrepaymentPremiumRatePeriodThreeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_CommonStockSharePricePercentageOfAverageDailyVolume_c991e242-8462-4f05-931d-eb64f6ef0908_terseLabel_en-US" xlink:label="lab_tlsi_CommonStockSharePricePercentageOfAverageDailyVolume" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchase agreement, maximum shares allowed, percentage of average daily volume</link:label>
    <link:label id="lab_tlsi_CommonStockSharePricePercentageOfAverageDailyVolume_label_en-US" xlink:label="lab_tlsi_CommonStockSharePricePercentageOfAverageDailyVolume" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Share Price, Percentage Of Average Daily Volume</link:label>
    <link:label id="lab_tlsi_CommonStockSharePricePercentageOfAverageDailyVolume_documentation_en-US" xlink:label="lab_tlsi_CommonStockSharePricePercentageOfAverageDailyVolume" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock, Share Price, Percentage Of Average Daily Volume</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_CommonStockSharePricePercentageOfAverageDailyVolume" xlink:href="tlsi-20250331.xsd#tlsi_CommonStockSharePricePercentageOfAverageDailyVolume"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_CommonStockSharePricePercentageOfAverageDailyVolume" xlink:to="lab_tlsi_CommonStockSharePricePercentageOfAverageDailyVolume" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_5e42406d-cd8d-4d94-bd2c-00d056ba01df_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instruments</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:to="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromStockOptionsExercised_70c43b01-7903-4346-89c4-dc4be6275439_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from the exercise of stock options for common stock</link:label>
    <link:label id="lab_us-gaap_ProceedsFromStockOptionsExercised_label_en-US" xlink:label="lab_us-gaap_ProceedsFromStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Stock Options Exercised</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromStockOptionsExercised" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ProceedsFromStockOptionsExercised"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromStockOptionsExercised" xlink:to="lab_us-gaap_ProceedsFromStockOptionsExercised" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_SPACWarrantsMember_a16a0e55-5286-41b9-a1ae-650f427301a5_terseLabel_en-US" xlink:label="lab_tlsi_SPACWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SPAC Warrants</link:label>
    <link:label id="lab_tlsi_SPACWarrantsMember_label_en-US" xlink:label="lab_tlsi_SPACWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SPAC Warrants [Member]</link:label>
    <link:label id="lab_tlsi_SPACWarrantsMember_documentation_en-US" xlink:label="lab_tlsi_SPACWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">SPAC Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SPACWarrantsMember" xlink:href="tlsi-20250331.xsd#tlsi_SPACWarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_SPACWarrantsMember" xlink:to="lab_tlsi_SPACWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgDiscLineItems_label_en-US" xlink:label="lab_ecd_AwardTmgDiscLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Disclosures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgDiscLineItems" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AwardTmgDiscLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgDiscLineItems" xlink:to="lab_ecd_AwardTmgDiscLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeGainLossOnDerivativeNet_4efeb9c9-3e33-49e2-a2e7-34b9b41eb97c_negatedLabel_en-US" xlink:label="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of warrants and SEPA liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeGainLossOnDerivativeNet_772de6fb-7502-4b81-8f01-d24aae97fc6c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Loss on change in fair value</link:label>
    <link:label id="lab_us-gaap_DerivativeGainLossOnDerivativeNet_label_en-US" xlink:label="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Gain (Loss) on Derivative, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativeGainLossOnDerivativeNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:to="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_label_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OtherPerfMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_OtherPerfMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OtherPerfMeasureAmt" xlink:to="lab_ecd_OtherPerfMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearPercentageOfStockFullyDiluted_adca8ebc-42b0-4111-868b-43ed38e11063_terseLabel_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearPercentageOfStockFullyDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share reserve increase, percentage of common stock</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearPercentageOfStockFullyDiluted_label_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearPercentageOfStockFullyDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Automatic Increase Per Year, Percentage Of Stock, Fully Diluted</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearPercentageOfStockFullyDiluted_documentation_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearPercentageOfStockFullyDiluted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Automatic Increase Per Year, Percentage Of Stock, Fully Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearPercentageOfStockFullyDiluted" xlink:href="tlsi-20250331.xsd#tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearPercentageOfStockFullyDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearPercentageOfStockFullyDiluted" xlink:to="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearPercentageOfStockFullyDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeasesTextBlock_7166b0e8-7df3-4d03-a4d1-f9a9493ad899_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeasesTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Leases [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeasesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeasesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeasesTextBlock" xlink:to="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_30fb7cff-9982-4262-a456-692546b806f5_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_ad5be6b5-cdae-4e05-82aa-b093afca2ac5_periodStartLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balances, beginning of period (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_dc07f8e5-e223-4f73-a12f-791291f8db7e_periodEndLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Balances, end of period (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightAxis_60bf9233-a5b7-45e4-8082-e86bddbb8ab3_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Axis]</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightAxis_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfWarrantOrRightAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightAxis" xlink:to="lab_us-gaap_ClassOfWarrantOrRightAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_98feee22-cff6-40fe-9d7f-8f92fcfb6ebd_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Available for Issue (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Available for Grant</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract_19aa3108-9c98-48d7-8915-cf02764a3e71_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from financing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Financing Activities, Continuing Operations [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock_9bc5774a-07a1-4206-8b39-8ec9c34a0305_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting</link:label>
    <link:label id="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SegmentReportingPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:to="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WarrantsAndRightsOutstandingTerm_72c82565-befb-49b8-8a73-a8421813fafe_verboseLabel_en-US" xlink:label="lab_us-gaap_WarrantsAndRightsOutstandingTerm" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Warrants, term</link:label>
    <link:label id="lab_us-gaap_WarrantsAndRightsOutstandingTerm_722671da-18b0-4d00-aaf9-da0fd8029ccd_terseLabel_en-US" xlink:label="lab_us-gaap_WarrantsAndRightsOutstandingTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnout shares vesting requirement, vesting period</link:label>
    <link:label id="lab_us-gaap_WarrantsAndRightsOutstandingTerm_label_en-US" xlink:label="lab_us-gaap_WarrantsAndRightsOutstandingTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrants and Rights Outstanding, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WarrantsAndRightsOutstandingTerm" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_WarrantsAndRightsOutstandingTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WarrantsAndRightsOutstandingTerm" xlink:to="lab_us-gaap_WarrantsAndRightsOutstandingTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PreferredStockIssuedPricePerShare_f7bfaf1f-409e-4845-a8ec-90cb1d3d3c88_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockIssuedPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Original issue price (in dollars per share)</link:label>
    <link:label id="lab_tlsi_PreferredStockIssuedPricePerShare_label_en-US" xlink:label="lab_tlsi_PreferredStockIssuedPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Issued Price Per Share</link:label>
    <link:label id="lab_tlsi_PreferredStockIssuedPricePerShare_documentation_en-US" xlink:label="lab_tlsi_PreferredStockIssuedPricePerShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Stock, Issued Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PreferredStockIssuedPricePerShare" xlink:href="tlsi-20250331.xsd#tlsi_PreferredStockIssuedPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PreferredStockIssuedPricePerShare" xlink:to="lab_tlsi_PreferredStockIssuedPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PlanNameDomain_3e854910-0853-4a2a-9429-34a9ba26e4c6_terseLabel_en-US" xlink:label="lab_us-gaap_PlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Plan Name [Domain]</link:label>
    <link:label id="lab_us-gaap_PlanNameDomain_label_en-US" xlink:label="lab_us-gaap_PlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Plan Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PlanNameDomain" xlink:to="lab_us-gaap_PlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DebtInstrumentPaidInKindInterestPercentage_58aa5583-17e8-439c-8745-86de4b562123_terseLabel_en-US" xlink:label="lab_tlsi_DebtInstrumentPaidInKindInterestPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Paid-in-kind interest</link:label>
    <link:label id="lab_tlsi_DebtInstrumentPaidInKindInterestPercentage_label_en-US" xlink:label="lab_tlsi_DebtInstrumentPaidInKindInterestPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Paid-In-Kind Interest Percentage</link:label>
    <link:label id="lab_tlsi_DebtInstrumentPaidInKindInterestPercentage_documentation_en-US" xlink:label="lab_tlsi_DebtInstrumentPaidInKindInterestPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Paid-In-Kind Interest Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DebtInstrumentPaidInKindInterestPercentage" xlink:href="tlsi-20250331.xsd#tlsi_DebtInstrumentPaidInKindInterestPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DebtInstrumentPaidInKindInterestPercentage" xlink:to="lab_tlsi_DebtInstrumentPaidInKindInterestPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockPricePerShare_584ef6cf-cc5c-47d2-bcc5-7d5cf1e207f8_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of stock, price per share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_SaleOfStockPricePerShare_label_en-US" xlink:label="lab_us-gaap_SaleOfStockPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockPricePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SaleOfStockPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockPricePerShare" xlink:to="lab_us-gaap_SaleOfStockPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_FairValueMeasurementReconciliationLiabilityValue_d193a6a8-e11d-41c9-b4f4-d83f546cbdd3_periodStartLabel_en-US" xlink:label="lab_tlsi_FairValueMeasurementReconciliationLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_tlsi_FairValueMeasurementReconciliationLiabilityValue_b70a390a-d725-405e-a28f-fb61aff3ab09_periodEndLabel_en-US" xlink:label="lab_tlsi_FairValueMeasurementReconciliationLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_tlsi_FairValueMeasurementReconciliationLiabilityValue_label_en-US" xlink:label="lab_tlsi_FairValueMeasurementReconciliationLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement Reconciliation, Liability Value</link:label>
    <link:label id="lab_tlsi_FairValueMeasurementReconciliationLiabilityValue_documentation_en-US" xlink:label="lab_tlsi_FairValueMeasurementReconciliationLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement Reconciliation, Liability Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_FairValueMeasurementReconciliationLiabilityValue" xlink:href="tlsi-20250331.xsd#tlsi_FairValueMeasurementReconciliationLiabilityValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_FairValueMeasurementReconciliationLiabilityValue" xlink:to="lab_tlsi_FairValueMeasurementReconciliationLiabilityValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockLiquidationPreference_c436a047-5d35-43b6-9d66-acc8d22df691_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockLiquidationPreference" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liquidation preference (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockLiquidationPreference_label_en-US" xlink:label="lab_us-gaap_PreferredStockLiquidationPreference" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Liquidation Preference Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockLiquidationPreference" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockLiquidationPreference"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockLiquidationPreference" xlink:to="lab_us-gaap_PreferredStockLiquidationPreference" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_df0e022d-2b7c-4f77-96ea-18f167d6b1f0_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_label_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherAssetsNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsNoncurrent" xlink:to="lab_us-gaap_OtherAssetsNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_14a59d43-7823-4a91-8ea2-448427306d65_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_label_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityTaxIdentificationNumber" xlink:to="lab_dei_EntityTaxIdentificationNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeasesAbstract_label_en-US" xlink:label="lab_us-gaap_LeasesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leases [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeasesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LeasesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeasesAbstract" xlink:to="lab_us-gaap_LeasesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_WarrantLiabilityPolicyPolicyTextBlock_a2f1868f-d40b-4d9f-b65a-fc8d04b5d833_terseLabel_en-US" xlink:label="lab_tlsi_WarrantLiabilityPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants Liabilities</link:label>
    <link:label id="lab_tlsi_WarrantLiabilityPolicyPolicyTextBlock_label_en-US" xlink:label="lab_tlsi_WarrantLiabilityPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrant Liability, Policy [Policy Text Block]</link:label>
    <link:label id="lab_tlsi_WarrantLiabilityPolicyPolicyTextBlock_documentation_en-US" xlink:label="lab_tlsi_WarrantLiabilityPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Warrant Liability, Policy</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_WarrantLiabilityPolicyPolicyTextBlock" xlink:href="tlsi-20250331.xsd#tlsi_WarrantLiabilityPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_WarrantLiabilityPolicyPolicyTextBlock" xlink:to="lab_tlsi_WarrantLiabilityPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock_0a27683f-fabf-46f2-b093-4034af6bb139_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfDebtInstrumentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_0b59b5f8-5143-4068-9a58-0481bf7ae2d9_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AntidilutiveSecuritiesNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:to="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAmountOfSharesAuthorized_bb2899e6-ddb5-4e3e-9785-dd8ace0d3071_terseLabel_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAmountOfSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum shares of common stock allowed under Purchase Agreement (in shares)</link:label>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAmountOfSharesAuthorized_label_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAmountOfSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Standby Equity Purchase Agreement, Maximum Amount Of Shares Authorized</link:label>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAmountOfSharesAuthorized_documentation_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAmountOfSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Standby Equity Purchase Agreement, Maximum Amount Of Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_StandbyEquityPurchaseAgreementMaximumAmountOfSharesAuthorized" xlink:href="tlsi-20250331.xsd#tlsi_StandbyEquityPurchaseAgreementMaximumAmountOfSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_StandbyEquityPurchaseAgreementMaximumAmountOfSharesAuthorized" xlink:to="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAmountOfSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_8639f3b8-6d48-4287-805f-f76361643ce8_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash used in operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_0a7461e0-2cb1-47fd-96a4-45e144dd1fd5_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net cash used in operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Operating Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction_46cf0d31-6c05-47c0-a029-33f18c1ca6ef_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of stock, consideration received on transaction</link:label>
    <link:label id="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction_label_en-US" xlink:label="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Consideration Received on Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SaleOfStockConsiderationReceivedOnTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:to="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_850010b8-178a-4cd6-b0a0-d22d6c2a6186_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from operating activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Operating Activities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuredDebtMember_33d15e74-1672-4934-8c72-63b7219bdcc4_terseLabel_en-US" xlink:label="lab_us-gaap_SecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Secured Debt</link:label>
    <link:label id="lab_us-gaap_SecuredDebtMember_label_en-US" xlink:label="lab_us-gaap_SecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secured Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuredDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SecuredDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuredDebtMember" xlink:to="lab_us-gaap_SecuredDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PlanNameAxis_8e361e4f-51e9-4540-a7c0-acab115901a5_terseLabel_en-US" xlink:label="lab_us-gaap_PlanNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Plan Name [Axis]</link:label>
    <link:label id="lab_us-gaap_PlanNameAxis_label_en-US" xlink:label="lab_us-gaap_PlanNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Plan Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PlanNameAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PlanNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PlanNameAxis" xlink:to="lab_us-gaap_PlanNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrepaidExpenseCurrent_240f6235-3426-488d-8e4c-917e2319d11d_terseLabel_en-US" xlink:label="lab_us-gaap_PrepaidExpenseCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepaid expenses</link:label>
    <link:label id="lab_us-gaap_PrepaidExpenseCurrent_label_en-US" xlink:label="lab_us-gaap_PrepaidExpenseCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepaid Expense, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidExpenseCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PrepaidExpenseCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrepaidExpenseCurrent" xlink:to="lab_us-gaap_PrepaidExpenseCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_6df77408-4c4d-456b-ab7a-382f5e569884_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightRedemptionPrice_2a434954-d2a2-49bb-a714-a47b1bb87a7c_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightRedemptionPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of warrant or right, redemption price (in dollars per share)</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightRedemptionPrice_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightRedemptionPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Redemption Price</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightRedemptionPrice_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightRedemptionPrice" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Redemption Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightRedemptionPrice" xlink:href="tlsi-20250331.xsd#tlsi_ClassOfWarrantOrRightRedemptionPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightRedemptionPrice" xlink:to="lab_tlsi_ClassOfWarrantOrRightRedemptionPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Method</link:label>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AwardTmgMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMethodTextBlock" xlink:to="lab_ecd_AwardTmgMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ResearchAndDevelopmentExpensePolicy_1b0f6ca3-6158-431d-8c3e-721301513111_terseLabel_en-US" xlink:label="lab_us-gaap_ResearchAndDevelopmentExpensePolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Research and Development</link:label>
    <link:label id="lab_us-gaap_ResearchAndDevelopmentExpensePolicy_label_en-US" xlink:label="lab_us-gaap_ResearchAndDevelopmentExpensePolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Research and Development Expense, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ResearchAndDevelopmentExpensePolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ResearchAndDevelopmentExpensePolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ResearchAndDevelopmentExpensePolicy" xlink:to="lab_us-gaap_ResearchAndDevelopmentExpensePolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TradingArrByIndTable_terseLabel_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual</link:label>
    <link:label id="lab_ecd_TradingArrByIndTable_label_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrByIndTable" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_TradingArrByIndTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrByIndTable" xlink:to="lab_ecd_TradingArrByIndTable" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodFiveMember_09e0be00-93ef-4441-96a7-24a8ef13c1f1_terseLabel_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodFiveMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">March 31, 2026</link:label>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodFiveMember_label_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodFiveMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Feature, Period Five [Member]</link:label>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodFiveMember_documentation_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodFiveMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Feature, Period Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_RevenueBaseRedemptionFeaturePeriodFiveMember" xlink:href="tlsi-20250331.xsd#tlsi_RevenueBaseRedemptionFeaturePeriodFiveMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_RevenueBaseRedemptionFeaturePeriodFiveMember" xlink:to="lab_tlsi_RevenueBaseRedemptionFeaturePeriodFiveMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TradeAndOtherAccountsReceivablePolicy_50a1dc14-92e6-4f7f-bc62-e9c49c8e22d1_terseLabel_en-US" xlink:label="lab_us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts Receivable and Customer Concentrations</link:label>
    <link:label id="lab_us-gaap_TradeAndOtherAccountsReceivablePolicy_label_en-US" xlink:label="lab_us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TradeAndOtherAccountsReceivablePolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:to="lab_us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_207e5b3a-fad5-4295-81dd-0133156522ac_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCommonStockSharesOutstanding" xlink:to="lab_dei_EntityCommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingPoliciesProcLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_InsiderTradingPoliciesProcLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:to="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UseOfEstimates_fc2d23ee-58a3-4ee5-a7b2-d61ce77dd044_terseLabel_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Use of Estimates</link:label>
    <link:label id="lab_us-gaap_UseOfEstimates_label_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Use of Estimates, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UseOfEstimates" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_UseOfEstimates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UseOfEstimates" xlink:to="lab_us-gaap_UseOfEstimates" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation, Amount</link:label>
    <link:label id="lab_ecd_AdjToCompAmt_label_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AdjToCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAmt" xlink:to="lab_ecd_AdjToCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PayablesAndAccrualsAbstract_label_en-US" xlink:label="lab_us-gaap_PayablesAndAccrualsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payables and Accruals [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PayablesAndAccrualsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PayablesAndAccrualsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PayablesAndAccrualsAbstract" xlink:to="lab_us-gaap_PayablesAndAccrualsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_OutstandingRecoveryCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryCompAmt" xlink:to="lab_ecd_OutstandingRecoveryCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_459a7584-3717-47a2-8b02-81429d699b22_terseLabel_en-US" xlink:label="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental disclosures of non-cash items:</link:label>
    <link:label id="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Flow, Noncash Investing and Financing Activities Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:to="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitySmallBusiness_7407da99-df7b-42ee-b8bd-09a88edb6a6d_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitySmallBusiness" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntitySmallBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitySmallBusiness" xlink:to="lab_dei_EntitySmallBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock_94d890b3-8d76-4b69-a66c-a70e15f0146b_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued Liabilities</link:label>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable and Accrued Liabilities Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock" xlink:to="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_CoSelectedMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureAmt" xlink:to="lab_ecd_CoSelectedMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PreferredStockConversionPriceFloor_8d876f6a-1a64-425b-a2df-31d83e5b3f8b_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockConversionPriceFloor" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series A Convertible Preferred Stock, floor conversion price (in dollars per share)</link:label>
    <link:label id="lab_tlsi_PreferredStockConversionPriceFloor_label_en-US" xlink:label="lab_tlsi_PreferredStockConversionPriceFloor" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Conversion Price, Floor</link:label>
    <link:label id="lab_tlsi_PreferredStockConversionPriceFloor_documentation_en-US" xlink:label="lab_tlsi_PreferredStockConversionPriceFloor" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Stock, Conversion Price, Floor</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PreferredStockConversionPriceFloor" xlink:href="tlsi-20250331.xsd#tlsi_PreferredStockConversionPriceFloor"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PreferredStockConversionPriceFloor" xlink:to="lab_tlsi_PreferredStockConversionPriceFloor" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDebtIssuanceCosts_69cfbd54-dfc6-436d-9955-436cb594e0fb_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Debt issuance costs</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDebtIssuanceCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PaymentsOfDebtIssuanceCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:to="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TabularListTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tabular List, Table</link:label>
    <link:label id="lab_ecd_TabularListTableTextBlock_label_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tabular List [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TabularListTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_TabularListTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TabularListTableTextBlock" xlink:to="lab_ecd_TabularListTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodTwoMember_4e451265-16ce-494f-813a-5e72df0619cb_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tranche Two</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_03fb3d49-95f8-4fd8-925f-5c6f0b883d4f_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems"/>
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    <link:label id="lab_tlsi_ClassOfWarrantOrRightWarrantsExchanged_d0934bbe-e767-4b3e-9e23-b8f4768e6123_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightWarrantsExchanged" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of warrants exchanged (in shares)</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightWarrantsExchanged_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightWarrantsExchanged" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Warrants Exchanged</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightWarrantsExchanged_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightWarrantsExchanged" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Warrants Exchanged</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightWarrantsExchanged" xlink:href="tlsi-20250331.xsd#tlsi_ClassOfWarrantOrRightWarrantsExchanged"/>
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    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember"/>
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    <link:label id="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights_28ae82f1-1db2-413f-a8a2-93c4f89c6cfc_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants to purchase common stock (in shares)</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Number of Securities Called by Warrants or Rights</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights"/>
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    <link:label id="lab_us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock_4d894d4b-7a61-463d-8377-23808c97d1d1_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss</link:label>
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    <link:label id="lab_us-gaap_LesseeLeaseDescriptionLineItems_1700dedd-42f2-4e2a-af66-41dd88aadc54_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Line Items]</link:label>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionLineItems_label_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeLeaseDescriptionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeLeaseDescriptionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeLeaseDescriptionLineItems" xlink:to="lab_us-gaap_LesseeLeaseDescriptionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrent_c603520e-85eb-41b5-82bb-cbdb6477fcb1_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued liabilities</link:label>
    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrent_ab4cf997-24ef-4fcc-b06b-1c39a67d3edd_totalLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total accrued liabilities</link:label>
    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccruedLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedLiabilitiesCurrent" xlink:to="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount"/>
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    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchasesSalesIssuancesSettlements_ff81b35d-9a54-4f49-aa38-dc9ca4832c5d_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchasesSalesIssuancesSettlements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuances (Settlements)</link:label>
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    <link:label id="lab_us-gaap_MeasurementInputExpectedDividendRateMember_0c50edcc-863e-4d5c-9287-1052944a87d3_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputExpectedDividendRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Estimated dividend yield</link:label>
    <link:label id="lab_us-gaap_MeasurementInputExpectedDividendRateMember_b7d9af9c-ac87-4589-9a68-82ec2ff2847c_verboseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputExpectedDividendRateMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Dividend yield</link:label>
    <link:label id="lab_us-gaap_MeasurementInputExpectedDividendRateMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputExpectedDividendRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Expected Dividend Rate [Member]</link:label>
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    <link:label id="lab_us-gaap_ClassOfWarrantOrRightLineItems_c8946304-4dec-4d8c-9b0c-c32650eb2567_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Line Items]</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightLineItems_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfWarrantOrRightLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightLineItems" xlink:to="lab_us-gaap_ClassOfWarrantOrRightLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock_13b18801-dde5-4230-8d28-3e0a564e28d8_terseLabel_en-US" xlink:label="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Impairment and Disposal of Long-Lived Assets</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock"/>
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    <link:label id="lab_us-gaap_AccruedBonusesCurrent_838af3a8-01b3-4953-ae69-4885ff1ad495_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedBonusesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued incentives</link:label>
    <link:label id="lab_us-gaap_AccruedBonusesCurrent_label_en-US" xlink:label="lab_us-gaap_AccruedBonusesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Bonuses, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedBonusesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccruedBonusesCurrent"/>
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    <link:label id="lab_us-gaap_AssetAcquisitionAxis_e0b923df-ac66-45e1-acef-19f32b2a1698_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Axis]</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionAxis_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PrivatePlacementAndWorkingCapitalWarrantsMember_0fb78dd3-a8ba-40bd-bb93-3463269b389a_terseLabel_en-US" xlink:label="lab_tlsi_PrivatePlacementAndWorkingCapitalWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private Placement And Working Capital Warrants</link:label>
    <link:label id="lab_tlsi_PrivatePlacementAndWorkingCapitalWarrantsMember_label_en-US" xlink:label="lab_tlsi_PrivatePlacementAndWorkingCapitalWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Private Placement And Working Capital Warrants [Member]</link:label>
    <link:label id="lab_tlsi_PrivatePlacementAndWorkingCapitalWarrantsMember_documentation_en-US" xlink:label="lab_tlsi_PrivatePlacementAndWorkingCapitalWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Private Placement And Working Capital Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PrivatePlacementAndWorkingCapitalWarrantsMember" xlink:href="tlsi-20250331.xsd#tlsi_PrivatePlacementAndWorkingCapitalWarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PrivatePlacementAndWorkingCapitalWarrantsMember" xlink:to="lab_tlsi_PrivatePlacementAndWorkingCapitalWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_LesseeNumberOfOperatingLeases_f28c08ba-fcaa-4132-bb1b-dac910292bbb_terseLabel_en-US" xlink:label="lab_tlsi_LesseeNumberOfOperatingLeases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of leases</link:label>
    <link:label id="lab_tlsi_LesseeNumberOfOperatingLeases_label_en-US" xlink:label="lab_tlsi_LesseeNumberOfOperatingLeases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Number Of Operating Leases</link:label>
    <link:label id="lab_tlsi_LesseeNumberOfOperatingLeases_documentation_en-US" xlink:label="lab_tlsi_LesseeNumberOfOperatingLeases" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Number Of Operating Leases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_LesseeNumberOfOperatingLeases" xlink:href="tlsi-20250331.xsd#tlsi_LesseeNumberOfOperatingLeases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_LesseeNumberOfOperatingLeases" xlink:to="lab_tlsi_LesseeNumberOfOperatingLeases" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_WarrantsAndRightsOutstandingNetOfIssuanceCosts_045684aa-4964-4553-b146-dfe63ee7170f_terseLabel_en-US" xlink:label="lab_tlsi_WarrantsAndRightsOutstandingNetOfIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants and rights outstanding, net of issuance costs</link:label>
    <link:label id="lab_tlsi_WarrantsAndRightsOutstandingNetOfIssuanceCosts_label_en-US" xlink:label="lab_tlsi_WarrantsAndRightsOutstandingNetOfIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrants and Rights Outstanding, Net Of Issuance Costs</link:label>
    <link:label id="lab_tlsi_WarrantsAndRightsOutstandingNetOfIssuanceCosts_documentation_en-US" xlink:label="lab_tlsi_WarrantsAndRightsOutstandingNetOfIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Warrants and Rights Outstanding, Net Of Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_WarrantsAndRightsOutstandingNetOfIssuanceCosts" xlink:href="tlsi-20250331.xsd#tlsi_WarrantsAndRightsOutstandingNetOfIssuanceCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_WarrantsAndRightsOutstandingNetOfIssuanceCosts" xlink:to="lab_tlsi_WarrantsAndRightsOutstandingNetOfIssuanceCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ProductRevenueBaseRedemptionMember_7cb4be24-02f5-496b-97ce-d61439b255e4_terseLabel_en-US" xlink:label="lab_tlsi_ProductRevenueBaseRedemptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue base redemption liability</link:label>
    <link:label id="lab_tlsi_ProductRevenueBaseRedemptionMember_label_en-US" xlink:label="lab_tlsi_ProductRevenueBaseRedemptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product Revenue Base Redemption [Member]</link:label>
    <link:label id="lab_tlsi_ProductRevenueBaseRedemptionMember_documentation_en-US" xlink:label="lab_tlsi_ProductRevenueBaseRedemptionMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Product Revenue Base Redemption</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ProductRevenueBaseRedemptionMember" xlink:href="tlsi-20250331.xsd#tlsi_ProductRevenueBaseRedemptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ProductRevenueBaseRedemptionMember" xlink:to="lab_tlsi_ProductRevenueBaseRedemptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_473dd965-f5a5-4399-82e1-e4e831c04d5a_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecognized compensation expense</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:to="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDepositsOutstanding_eb64e3cf-0632-48d2-abd4-0a02b68056c1_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDepositsOutstanding" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Deposits</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDepositsOutstanding_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDepositsOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Deposits Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInDepositsOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncreaseDecreaseInDepositsOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInDepositsOutstanding" xlink:to="lab_us-gaap_IncreaseDecreaseInDepositsOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsCurrentAbstract_9db6dc36-57d2-4ca8-9194-b803d95b3c77_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current assets:</link:label>
    <link:label id="lab_us-gaap_AssetsCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Current [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AssetsCurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsCurrentAbstract" xlink:to="lab_us-gaap_AssetsCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightWarrantsExercised_959f63a8-d3a3-461c-9289-082e806478c5_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightWarrantsExercised" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercises (in shares)</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightWarrantsExercised_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightWarrantsExercised" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Warrants Exercised</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightWarrantsExercised_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightWarrantsExercised" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Warrants Exercised</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightWarrantsExercised" xlink:href="tlsi-20250331.xsd#tlsi_ClassOfWarrantOrRightWarrantsExercised"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightWarrantsExercised" xlink:to="lab_tlsi_ClassOfWarrantOrRightWarrantsExercised" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionDaysNotice_b3858198-ce99-499d-a6af-852b7bf48600_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionDaysNotice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Threshold number of business days before sending notice of redemption to warrant holders</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionDaysNotice_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionDaysNotice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Conversion Days Notice</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionDaysNotice_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionDaysNotice" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Conversion Days Notice</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightConversionDaysNotice" xlink:href="tlsi-20250331.xsd#tlsi_ClassOfWarrantOrRightConversionDaysNotice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightConversionDaysNotice" xlink:to="lab_tlsi_ClassOfWarrantOrRightConversionDaysNotice" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PrivateWarrantsMember_f94e48b3-24a5-4011-9c16-0928225ffd7c_terseLabel_en-US" xlink:label="lab_tlsi_PrivateWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private Placement Warrants</link:label>
    <link:label id="lab_tlsi_PrivateWarrantsMember_label_en-US" xlink:label="lab_tlsi_PrivateWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Private Warrants [Member]</link:label>
    <link:label id="lab_tlsi_PrivateWarrantsMember_documentation_en-US" xlink:label="lab_tlsi_PrivateWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Private Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PrivateWarrantsMember" xlink:href="tlsi-20250331.xsd#tlsi_PrivateWarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PrivateWarrantsMember" xlink:to="lab_tlsi_PrivateWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryDisclosureTextBlock_45d19376-7a60-41c3-92e0-fa6a33e075a8_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Inventory</link:label>
    <link:label id="lab_us-gaap_InventoryDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_InventoryDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InventoryDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryDisclosureTextBlock" xlink:to="lab_us-gaap_InventoryDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_NatureOfBusinessTable_15d8020e-2d81-4fb9-880d-5d0054d88d88_terseLabel_en-US" xlink:label="lab_tlsi_NatureOfBusinessTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nature of Business [Table]</link:label>
    <link:label id="lab_tlsi_NatureOfBusinessTable_label_en-US" xlink:label="lab_tlsi_NatureOfBusinessTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nature of Business [Table]</link:label>
    <link:label id="lab_tlsi_NatureOfBusinessTable_documentation_en-US" xlink:label="lab_tlsi_NatureOfBusinessTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Nature of Business [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_NatureOfBusinessTable" xlink:href="tlsi-20250331.xsd#tlsi_NatureOfBusinessTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_NatureOfBusinessTable" xlink:to="lab_tlsi_NatureOfBusinessTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DebtInstrumentDebtDefaultRate_7be33c3b-54e9-4177-9858-6990df8b4c4f_terseLabel_en-US" xlink:label="lab_tlsi_DebtInstrumentDebtDefaultRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Default rate</link:label>
    <link:label id="lab_tlsi_DebtInstrumentDebtDefaultRate_label_en-US" xlink:label="lab_tlsi_DebtInstrumentDebtDefaultRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Debt Default, Rate</link:label>
    <link:label id="lab_tlsi_DebtInstrumentDebtDefaultRate_documentation_en-US" xlink:label="lab_tlsi_DebtInstrumentDebtDefaultRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Debt Default, Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DebtInstrumentDebtDefaultRate" xlink:href="tlsi-20250331.xsd#tlsi_DebtInstrumentDebtDefaultRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DebtInstrumentDebtDefaultRate" xlink:to="lab_tlsi_DebtInstrumentDebtDefaultRate" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInformationLineItems_1cb9258c-863b-4e25-88f7-309ebd5112cf_terseLabel_en-US" xlink:label="lab_dei_EntityInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Information [Line Items]</link:label>
    <link:label id="lab_dei_EntityInformationLineItems_label_en-US" xlink:label="lab_dei_EntityInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInformationLineItems" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInformationLineItems" xlink:to="lab_dei_EntityInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_d50797f8-18cf-4116-93c1-720c4a0324b6_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Options to purchase common stock</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_b5d253cc-e664-4289-8737-0da95c712cb9_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:to="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedIncomeTaxesCurrent_870d5bf3-dc80-4489-a1a8-60a1e6d0ac2d_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedIncomeTaxesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued taxes</link:label>
    <link:label id="lab_us-gaap_AccruedIncomeTaxesCurrent_label_en-US" xlink:label="lab_us-gaap_AccruedIncomeTaxesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Income Taxes, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedIncomeTaxesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccruedIncomeTaxesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedIncomeTaxesCurrent" xlink:to="lab_us-gaap_AccruedIncomeTaxesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_ec9d0428-4de2-4a33-8225-62cd612058ca_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_03fcaa40-6a72-4bca-a603-f414d0206af2_periodStartLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_33a1d8a3-9543-49f1-a6f3-c6d8297002a0_periodEndLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesOutstanding" xlink:to="lab_us-gaap_PreferredStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_cd5e5fd9-3b67-4c70-836d-cdd0d71b3c44_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_SecurityExchangeName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_SecurityExchangeName" xlink:to="lab_dei_SecurityExchangeName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WarrantMember_cdf82142-cc80-4dfe-8df2-7cf88050abc8_terseLabel_en-US" xlink:label="lab_us-gaap_WarrantMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants</link:label>
    <link:label id="lab_us-gaap_WarrantMember_label_en-US" xlink:label="lab_us-gaap_WarrantMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrant [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WarrantMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_WarrantMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WarrantMember" xlink:to="lab_us-gaap_WarrantMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaidInKindInterest_2d825f82-4f9e-4fa4-843b-a16e80666cbd_verboseLabel_en-US" xlink:label="lab_us-gaap_PaidInKindInterest" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">PIK interest</link:label>
    <link:label id="lab_us-gaap_PaidInKindInterest_0adf3a3f-f39c-48b7-a5a0-1e009e0010ba_terseLabel_en-US" xlink:label="lab_us-gaap_PaidInKindInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PIK interest</link:label>
    <link:label id="lab_us-gaap_PaidInKindInterest_label_en-US" xlink:label="lab_us-gaap_PaidInKindInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Paid-in-Kind Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaidInKindInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PaidInKindInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaidInKindInterest" xlink:to="lab_us-gaap_PaidInKindInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_382d8861-6838-4a96-bdc1-6a8e74b16a93_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, basis spread on variable rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Basis Spread on Variable Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentBasisSpreadOnVariableRate1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:to="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PreferredStockDividendsUndeclaredCumulativeDividends_b34a6f65-4c68-40e5-b81d-c80c7e7eacc8_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockDividendsUndeclaredCumulativeDividends" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Undeclared cumulative dividends</link:label>
    <link:label id="lab_tlsi_PreferredStockDividendsUndeclaredCumulativeDividends_label_en-US" xlink:label="lab_tlsi_PreferredStockDividendsUndeclaredCumulativeDividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock Dividends, Undeclared Cumulative Dividends</link:label>
    <link:label id="lab_tlsi_PreferredStockDividendsUndeclaredCumulativeDividends_documentation_en-US" xlink:label="lab_tlsi_PreferredStockDividendsUndeclaredCumulativeDividends" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Stock Dividends, Undeclared Cumulative Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PreferredStockDividendsUndeclaredCumulativeDividends" xlink:href="tlsi-20250331.xsd#tlsi_PreferredStockDividendsUndeclaredCumulativeDividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PreferredStockDividendsUndeclaredCumulativeDividends" xlink:to="lab_tlsi_PreferredStockDividendsUndeclaredCumulativeDividends" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AwardTypeAxis_7506f116-59d8-43f7-b793-33f82ae18867_terseLabel_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:label id="lab_us-gaap_AwardTypeAxis_label_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AwardTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AwardTypeAxis" xlink:to="lab_us-gaap_AwardTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_LesseeOperatingLeaseNumberOfRenewalOptionsExercised_08b5cd29-2b31-4781-9a56-3f5a69205346_terseLabel_en-US" xlink:label="lab_tlsi_LesseeOperatingLeaseNumberOfRenewalOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of lease renewal options exercised</link:label>
    <link:label id="lab_tlsi_LesseeOperatingLeaseNumberOfRenewalOptionsExercised_label_en-US" xlink:label="lab_tlsi_LesseeOperatingLeaseNumberOfRenewalOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Number Of Renewal Options Exercised</link:label>
    <link:label id="lab_tlsi_LesseeOperatingLeaseNumberOfRenewalOptionsExercised_documentation_en-US" xlink:label="lab_tlsi_LesseeOperatingLeaseNumberOfRenewalOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Number Of Renewal Options Exercised</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_LesseeOperatingLeaseNumberOfRenewalOptionsExercised" xlink:href="tlsi-20250331.xsd#tlsi_LesseeOperatingLeaseNumberOfRenewalOptionsExercised"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_LesseeOperatingLeaseNumberOfRenewalOptionsExercised" xlink:to="lab_tlsi_LesseeOperatingLeaseNumberOfRenewalOptionsExercised" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_CommonStockSharesAuthorizedStandbyEquityPurchaseAgreement_a1cd04bd-0fc4-41ba-b857-3ef67e4de217_terseLabel_en-US" xlink:label="lab_tlsi_CommonStockSharesAuthorizedStandbyEquityPurchaseAgreement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares authorized, standby equity purchase agreement (in shares)</link:label>
    <link:label id="lab_tlsi_CommonStockSharesAuthorizedStandbyEquityPurchaseAgreement_label_en-US" xlink:label="lab_tlsi_CommonStockSharesAuthorizedStandbyEquityPurchaseAgreement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized, Standby Equity Purchase Agreement</link:label>
    <link:label id="lab_tlsi_CommonStockSharesAuthorizedStandbyEquityPurchaseAgreement_documentation_en-US" xlink:label="lab_tlsi_CommonStockSharesAuthorizedStandbyEquityPurchaseAgreement" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized, Standby Equity Purchase Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_CommonStockSharesAuthorizedStandbyEquityPurchaseAgreement" xlink:href="tlsi-20250331.xsd#tlsi_CommonStockSharesAuthorizedStandbyEquityPurchaseAgreement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_CommonStockSharesAuthorizedStandbyEquityPurchaseAgreement" xlink:to="lab_tlsi_CommonStockSharesAuthorizedStandbyEquityPurchaseAgreement" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ContingentEarnoutLiabilityMember_cbb164aa-98b0-4be3-ba0c-c0c5fc8b69e4_terseLabel_en-US" xlink:label="lab_tlsi_ContingentEarnoutLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contingent earnout liability</link:label>
    <link:label id="lab_tlsi_ContingentEarnoutLiabilityMember_label_en-US" xlink:label="lab_tlsi_ContingentEarnoutLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contingent Earnout Liability [Member]</link:label>
    <link:label id="lab_tlsi_ContingentEarnoutLiabilityMember_documentation_en-US" xlink:label="lab_tlsi_ContingentEarnoutLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Contingent Earnout Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ContingentEarnoutLiabilityMember" xlink:href="tlsi-20250331.xsd#tlsi_ContingentEarnoutLiabilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ContingentEarnoutLiabilityMember" xlink:to="lab_tlsi_ContingentEarnoutLiabilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseContractualTermDomain_3ba24b15-9299-43e1-aa80-0e6c6bbd3998_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseContractualTermDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease Contractual Term [Domain]</link:label>
    <link:label id="lab_us-gaap_LeaseContractualTermDomain_label_en-US" xlink:label="lab_us-gaap_LeaseContractualTermDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease Contractual Term [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseContractualTermDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LeaseContractualTermDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseContractualTermDomain" xlink:to="lab_us-gaap_LeaseContractualTermDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdConsecutiveTradingDays_22601fe0-b41d-421e-ae9b-0b3ab14c9050_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of warrant or right, conversion terms, threshold consecutive trading days</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdConsecutiveTradingDays_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Conversion Terms, Threshold Consecutive Trading Days</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdConsecutiveTradingDays_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Conversion Terms, Threshold Consecutive Trading Days</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightConversionTermsThresholdConsecutiveTradingDays" xlink:href="tlsi-20250331.xsd#tlsi_ClassOfWarrantOrRightConversionTermsThresholdConsecutiveTradingDays"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightConversionTermsThresholdConsecutiveTradingDays" xlink:to="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdConsecutiveTradingDays" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Liabilities_be88c70c-7b42-434b-a783-75af36cc8b44_totalLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_label_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_Liabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Liabilities" xlink:to="lab_us-gaap_Liabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsIssued_6ad282fe-d14f-4147-90d7-f663ed63889a_terseLabel_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock options issued (in shares)</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsIssued_label_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Options, Issued</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsIssued_documentation_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsIssued" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Options, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsIssued" xlink:href="tlsi-20250331.xsd#tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsIssued" xlink:to="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock_9c6ddc4a-5dd5-4572-b275-f8bb89817b2c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Cash and Cash Equivalents</link:label>
    <link:label id="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Cash and Cash Equivalents [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_CommonStockPeriodIncreaseDecreaseInCapitalSharesReservedForFutureIssuance_946b8146-552d-43aa-8513-47921789441f_terseLabel_en-US" xlink:label="lab_tlsi_CommonStockPeriodIncreaseDecreaseInCapitalSharesReservedForFutureIssuance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase in common stock reserve for future issuance (in shares)</link:label>
    <link:label id="lab_tlsi_CommonStockPeriodIncreaseDecreaseInCapitalSharesReservedForFutureIssuance_label_en-US" xlink:label="lab_tlsi_CommonStockPeriodIncreaseDecreaseInCapitalSharesReservedForFutureIssuance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Period Increase (Decrease) in Capital Shares Reserved for Future Issuance</link:label>
    <link:label id="lab_tlsi_CommonStockPeriodIncreaseDecreaseInCapitalSharesReservedForFutureIssuance_documentation_en-US" xlink:label="lab_tlsi_CommonStockPeriodIncreaseDecreaseInCapitalSharesReservedForFutureIssuance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock, Period Increase (Decrease) In Capital Shares Reserved For Future Issuance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_CommonStockPeriodIncreaseDecreaseInCapitalSharesReservedForFutureIssuance" xlink:href="tlsi-20250331.xsd#tlsi_CommonStockPeriodIncreaseDecreaseInCapitalSharesReservedForFutureIssuance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_CommonStockPeriodIncreaseDecreaseInCapitalSharesReservedForFutureIssuance" xlink:to="lab_tlsi_CommonStockPeriodIncreaseDecreaseInCapitalSharesReservedForFutureIssuance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_753e2bbf-9792-41cc-8028-731ded7a6e22_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:to="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ResearchAndDevelopmentExpense_8afc9635-2972-489a-9981-1c83986fcc45_terseLabel_en-US" xlink:label="lab_us-gaap_ResearchAndDevelopmentExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Research and development</link:label>
    <link:label id="lab_us-gaap_ResearchAndDevelopmentExpense_label_en-US" xlink:label="lab_us-gaap_ResearchAndDevelopmentExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Research and Development Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ResearchAndDevelopmentExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ResearchAndDevelopmentExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ResearchAndDevelopmentExpense" xlink:to="lab_us-gaap_ResearchAndDevelopmentExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_f2dc71d9-d83a-4723-a18f-4a6b3f9fede7_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:to="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrExpirationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expiration Date</link:label>
    <link:label id="lab_ecd_TrdArrExpirationDate_label_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Expiration Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrExpirationDate" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_TrdArrExpirationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrExpirationDate" xlink:to="lab_ecd_TrdArrExpirationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_SharePriceAsPercentageOfMarketPriceWithAdvanceNoticeOptionTwo_bb6d802d-8653-461c-a0bb-061aee94b1ae_terseLabel_en-US" xlink:label="lab_tlsi_SharePriceAsPercentageOfMarketPriceWithAdvanceNoticeOptionTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchase agreement, sales price, percentage of market price during three consecutive trading days</link:label>
    <link:label id="lab_tlsi_SharePriceAsPercentageOfMarketPriceWithAdvanceNoticeOptionTwo_label_en-US" xlink:label="lab_tlsi_SharePriceAsPercentageOfMarketPriceWithAdvanceNoticeOptionTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Price As Percentage Of Market Price With Advance Notice, Option Two</link:label>
    <link:label id="lab_tlsi_SharePriceAsPercentageOfMarketPriceWithAdvanceNoticeOptionTwo_documentation_en-US" xlink:label="lab_tlsi_SharePriceAsPercentageOfMarketPriceWithAdvanceNoticeOptionTwo" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share Price As Percentage Of Market Price With Advance Notice, Option Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SharePriceAsPercentageOfMarketPriceWithAdvanceNoticeOptionTwo" xlink:href="tlsi-20250331.xsd#tlsi_SharePriceAsPercentageOfMarketPriceWithAdvanceNoticeOptionTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_SharePriceAsPercentageOfMarketPriceWithAdvanceNoticeOptionTwo" xlink:to="lab_tlsi_SharePriceAsPercentageOfMarketPriceWithAdvanceNoticeOptionTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock_bbc8fc2d-2d85-4aca-9985-ae263cfe734a_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from the issuance of preferred stock</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight_b9528b39-c40c-47e1-8def-f66c72e17354_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of warrant or right, number of securities called by each warrant or right (in shares)</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Number of Securities Called by Each Warrant or Right</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:to="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_TotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnAmt" xlink:to="lab_ecd_TotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_b44ea7e9-8794-433e-bedf-5c95de66acb0_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesIssued" xlink:to="lab_us-gaap_CommonStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_EqtyAwrdsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:to="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_9868bc49-f38e-40ab-95c5-e55303234c0a_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of credit maximum borrowing capacity</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_InsiderTrdPoliciesProcAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:to="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_LineOfCreditFacilityProductRevenueBaseMinimumThresholdAmount_8070f249-0e8c-4de0-8af9-e8765f4dc9dd_terseLabel_en-US" xlink:label="lab_tlsi_LineOfCreditFacilityProductRevenueBaseMinimumThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product revenue base, minimum amount required</link:label>
    <link:label id="lab_tlsi_LineOfCreditFacilityProductRevenueBaseMinimumThresholdAmount_label_en-US" xlink:label="lab_tlsi_LineOfCreditFacilityProductRevenueBaseMinimumThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line Of Credit Facility, Product Revenue Base, Minimum Threshold Amount</link:label>
    <link:label id="lab_tlsi_LineOfCreditFacilityProductRevenueBaseMinimumThresholdAmount_documentation_en-US" xlink:label="lab_tlsi_LineOfCreditFacilityProductRevenueBaseMinimumThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line Of Credit Facility, Product Revenue Base, Minimum Threshold Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_LineOfCreditFacilityProductRevenueBaseMinimumThresholdAmount" xlink:href="tlsi-20250331.xsd#tlsi_LineOfCreditFacilityProductRevenueBaseMinimumThresholdAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_LineOfCreditFacilityProductRevenueBaseMinimumThresholdAmount" xlink:to="lab_tlsi_LineOfCreditFacilityProductRevenueBaseMinimumThresholdAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_eee8f7b6-41a2-4e76-b470-762834602eba_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise of options (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercises in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_8fc8bb65-217d-40ec-bb37-e3993e843fcf_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_RevenueBaseRedemptionLiabilityPolicyPolicyTextBlock_d1ca0326-9de9-4957-ad99-a5c77b0198ca_terseLabel_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionLiabilityPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Liability</link:label>
    <link:label id="lab_tlsi_RevenueBaseRedemptionLiabilityPolicyPolicyTextBlock_label_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionLiabilityPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Liability, Policy [Policy Text Block]</link:label>
    <link:label id="lab_tlsi_RevenueBaseRedemptionLiabilityPolicyPolicyTextBlock_documentation_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionLiabilityPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Liability, Policy</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_RevenueBaseRedemptionLiabilityPolicyPolicyTextBlock" xlink:href="tlsi-20250331.xsd#tlsi_RevenueBaseRedemptionLiabilityPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_RevenueBaseRedemptionLiabilityPolicyPolicyTextBlock" xlink:to="lab_tlsi_RevenueBaseRedemptionLiabilityPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote</link:label>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_label_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_NamedExecutiveOfficersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:to="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_dcb8277f-2edc-4883-9765-8b1a688ac259_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesAuthorized" xlink:to="lab_us-gaap_CommonStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightTable_adfc45e1-18da-4f20-a2ea-aaef781d1950_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Table]</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightTable_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfWarrantOrRightTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightTable" xlink:to="lab_us-gaap_ClassOfWarrantOrRightTable" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_TemporaryEquityStockRetiredOrConvertedDuringPeriodShares_bdec43a2-4800-46c4-955c-915d7623fbb8_negatedTerseLabel_en-US" xlink:label="lab_tlsi_TemporaryEquityStockRetiredOrConvertedDuringPeriodShares" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Retirements/Conversions (in shares)</link:label>
    <link:label id="lab_tlsi_TemporaryEquityStockRetiredOrConvertedDuringPeriodShares_label_en-US" xlink:label="lab_tlsi_TemporaryEquityStockRetiredOrConvertedDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Stock Retired Or Converted During Period, Shares</link:label>
    <link:label id="lab_tlsi_TemporaryEquityStockRetiredOrConvertedDuringPeriodShares_documentation_en-US" xlink:label="lab_tlsi_TemporaryEquityStockRetiredOrConvertedDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Stock Retired Or Converted During Period, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_TemporaryEquityStockRetiredOrConvertedDuringPeriodShares" xlink:href="tlsi-20250331.xsd#tlsi_TemporaryEquityStockRetiredOrConvertedDuringPeriodShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_TemporaryEquityStockRetiredOrConvertedDuringPeriodShares" xlink:to="lab_tlsi_TemporaryEquityStockRetiredOrConvertedDuringPeriodShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_ef3dfd2a-7a97-4af6-bc77-8b828e2c1610_terseLabel_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basis of Presentation</link:label>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Basis of Accounting, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BasisOfAccountingPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:to="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_692277e4-fed1-4384-b3d4-e1843c1ccfb4_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average common shares outstanding, diluted (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_terseLabel_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value</link:label>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_label_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_MnpiDiscTimedForCompValFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:to="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_7a288743-df8c-4db4-a697-1cf4c41f590e_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightWarrantSplitNumberOfNewWarrants_ec70c544-f403-4e06-bb68-f9131a197a0c_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightWarrantSplitNumberOfNewWarrants" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of warrants after split</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightWarrantSplitNumberOfNewWarrants_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightWarrantSplitNumberOfNewWarrants" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Warrant Split, Number Of New Warrants</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightWarrantSplitNumberOfNewWarrants_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightWarrantSplitNumberOfNewWarrants" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Warrant Split, Number Of New Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightWarrantSplitNumberOfNewWarrants" xlink:href="tlsi-20250331.xsd#tlsi_ClassOfWarrantOrRightWarrantSplitNumberOfNewWarrants"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightWarrantSplitNumberOfNewWarrants" xlink:to="lab_tlsi_ClassOfWarrantOrRightWarrantSplitNumberOfNewWarrants" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_a997c132-ecff-42f8-abbe-7c385c38828e_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total stockholders&#8217; deficit</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_dd2426b7-e998-435f-9f0a-95c66c17f371_periodStartLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balance, beginning of period</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_f7781c69-9878-4836-a186-746505196057_periodEndLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Balance, end of period</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementSEPAMember_cdefa460-bcfe-49a9-9095-7d25e11c8d02_terseLabel_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementSEPAMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares issuable under the SEPA</link:label>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementSEPAMember_label_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementSEPAMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Standby Equity Purchase Agreement (SEPA) [Member]</link:label>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementSEPAMember_documentation_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementSEPAMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Standby Equity Purchase Agreement (SEPA)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_StandbyEquityPurchaseAgreementSEPAMember" xlink:href="tlsi-20250331.xsd#tlsi_StandbyEquityPurchaseAgreementSEPAMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_StandbyEquityPurchaseAgreementSEPAMember" xlink:to="lab_tlsi_StandbyEquityPurchaseAgreementSEPAMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilityMeasurementInput_42ed1374-97da-438c-bec4-b5e58b8fb7c3_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Expected draws</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityMeasurementInput_9bc65709-bd5e-4939-844c-cb6c1b32eb13_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative liability, measurement input</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityMeasurementInput_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativeLiabilityMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityMeasurementInput" xlink:to="lab_us-gaap_DerivativeLiabilityMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_AssetAcquisitionRoyaltyPercentageUnderThresholdAmount_776ae66f-baf0-4f2d-bd2f-881e5fe374fc_terseLabel_en-US" xlink:label="lab_tlsi_AssetAcquisitionRoyaltyPercentageUnderThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Royalties as a percentage of net sales, under sales threshold</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionRoyaltyPercentageUnderThresholdAmount_label_en-US" xlink:label="lab_tlsi_AssetAcquisitionRoyaltyPercentageUnderThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Royalty Percentage, Under Threshold Amount</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionRoyaltyPercentageUnderThresholdAmount_documentation_en-US" xlink:label="lab_tlsi_AssetAcquisitionRoyaltyPercentageUnderThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Royalty Percentage, Under Threshold Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_AssetAcquisitionRoyaltyPercentageUnderThresholdAmount" xlink:href="tlsi-20250331.xsd#tlsi_AssetAcquisitionRoyaltyPercentageUnderThresholdAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_AssetAcquisitionRoyaltyPercentageUnderThresholdAmount" xlink:to="lab_tlsi_AssetAcquisitionRoyaltyPercentageUnderThresholdAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseRenewalTerm_efb4e248-58c2-4da4-abb3-d87c46a34042_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseRenewalTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease renewal term</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseRenewalTerm_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseRenewalTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Renewal Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseRenewalTerm" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseRenewalTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseRenewalTerm" xlink:to="lab_us-gaap_LesseeOperatingLeaseRenewalTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_TemporaryEquitySharesIssuedDuringPeriod_09cf2f3f-956d-45ab-b1bc-ac43235fd025_terseLabel_en-US" xlink:label="lab_tlsi_TemporaryEquitySharesIssuedDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuances (in shares)</link:label>
    <link:label id="lab_tlsi_TemporaryEquitySharesIssuedDuringPeriod_label_en-US" xlink:label="lab_tlsi_TemporaryEquitySharesIssuedDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares Issued During Period</link:label>
    <link:label id="lab_tlsi_TemporaryEquitySharesIssuedDuringPeriod_documentation_en-US" xlink:label="lab_tlsi_TemporaryEquitySharesIssuedDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares Issued During Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_TemporaryEquitySharesIssuedDuringPeriod" xlink:href="tlsi-20250331.xsd#tlsi_TemporaryEquitySharesIssuedDuringPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_TemporaryEquitySharesIssuedDuringPeriod" xlink:to="lab_tlsi_TemporaryEquitySharesIssuedDuringPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract_96d160b8-e48c-40ed-939a-a7ad487a148e_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from investing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Investing Activities, Continuing Operations [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseNonoperating_487a1499-3a9c-4fa6-ae7f-f46ed5a3da71_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseNonoperating" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseNonoperating_label_en-US" xlink:label="lab_us-gaap_InterestExpenseNonoperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Nonoperating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseNonoperating" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InterestExpenseNonoperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseNonoperating" xlink:to="lab_us-gaap_InterestExpenseNonoperating" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_GainLossOnChangeInFairValueOfWarrantsAndOtherLiabilities_431bb479-e7ba-4e07-a4dd-581a1b1e57bf_terseLabel_en-US" xlink:label="lab_tlsi_GainLossOnChangeInFairValueOfWarrantsAndOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of SEPA, warrant, and revenue base redemption liabilities</link:label>
    <link:label id="lab_tlsi_GainLossOnChangeInFairValueOfWarrantsAndOtherLiabilities_label_en-US" xlink:label="lab_tlsi_GainLossOnChangeInFairValueOfWarrantsAndOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) On Change In Fair Value Of Warrants And Other Liabilities</link:label>
    <link:label id="lab_tlsi_GainLossOnChangeInFairValueOfWarrantsAndOtherLiabilities_documentation_en-US" xlink:label="lab_tlsi_GainLossOnChangeInFairValueOfWarrantsAndOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gain (Loss) On Change In Fair Value Of Warrants And Other Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_GainLossOnChangeInFairValueOfWarrantsAndOtherLiabilities" xlink:href="tlsi-20250331.xsd#tlsi_GainLossOnChangeInFairValueOfWarrantsAndOtherLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_GainLossOnChangeInFairValueOfWarrantsAndOtherLiabilities" xlink:to="lab_tlsi_GainLossOnChangeInFairValueOfWarrantsAndOtherLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedSalariesCurrent_111985c5-f178-4ac9-a392-ceee5e82aa69_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedSalariesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued payroll</link:label>
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    <link:label id="lab_us-gaap_LineOfCreditFacilityCommitmentFeePercentage_5c167b09-7d3d-48d8-95f4-a84f72816594_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityCommitmentFeePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitment fee percentage</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityCommitmentFeePercentage_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityCommitmentFeePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Commitment Fee Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityCommitmentFeePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LineOfCreditFacilityCommitmentFeePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityCommitmentFeePercentage" xlink:to="lab_us-gaap_LineOfCreditFacilityCommitmentFeePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TemporaryEquityDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityDisclosureAbstract" xlink:to="lab_us-gaap_TemporaryEquityDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PnsnBnftsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:to="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_TotalShareholderRtnVsPeerGroupTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:to="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_RecapitalizationExchangeRatio_1c1efe6c-9d70-4cdc-a6b9-d57ebc749bda_terseLabel_en-US" xlink:label="lab_tlsi_RecapitalizationExchangeRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exchange ratio (in shares)</link:label>
    <link:label id="lab_tlsi_RecapitalizationExchangeRatio_label_en-US" xlink:label="lab_tlsi_RecapitalizationExchangeRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recapitalization Exchange Ratio</link:label>
    <link:label id="lab_tlsi_RecapitalizationExchangeRatio_documentation_en-US" xlink:label="lab_tlsi_RecapitalizationExchangeRatio" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Recapitalization Exchange Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_RecapitalizationExchangeRatio" xlink:href="tlsi-20250331.xsd#tlsi_RecapitalizationExchangeRatio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_RecapitalizationExchangeRatio" xlink:to="lab_tlsi_RecapitalizationExchangeRatio" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent_373d346f-5236-4b8d-9491-d0f4c873c91e_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contingent earnout liability</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Contingent Consideration, Liability, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent" xlink:to="lab_us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodTwoMember_99d23a78-7696-4218-a9ad-8de05029b969_terseLabel_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">June 30, 2025</link:label>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodTwoMember_label_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Feature, Period Two [Member]</link:label>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodTwoMember_documentation_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Feature, Period Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_RevenueBaseRedemptionFeaturePeriodTwoMember" xlink:href="tlsi-20250331.xsd#tlsi_RevenueBaseRedemptionFeaturePeriodTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_RevenueBaseRedemptionFeaturePeriodTwoMember" xlink:to="lab_tlsi_RevenueBaseRedemptionFeaturePeriodTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_LesseeNumberOfFinanceLeases_16968a93-b0c9-4d9d-96ac-161f42830453_terseLabel_en-US" xlink:label="lab_tlsi_LesseeNumberOfFinanceLeases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee, number of finance leases</link:label>
    <link:label id="lab_tlsi_LesseeNumberOfFinanceLeases_label_en-US" xlink:label="lab_tlsi_LesseeNumberOfFinanceLeases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Number Of Finance Leases</link:label>
    <link:label id="lab_tlsi_LesseeNumberOfFinanceLeases_documentation_en-US" xlink:label="lab_tlsi_LesseeNumberOfFinanceLeases" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Number Of Finance Leases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_LesseeNumberOfFinanceLeases" xlink:href="tlsi-20250331.xsd#tlsi_LesseeNumberOfFinanceLeases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_LesseeNumberOfFinanceLeases" xlink:to="lab_tlsi_LesseeNumberOfFinanceLeases" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MaximumMember_c9294106-6633-4346-8e0a-ceb798bdb78e_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum</link:label>
    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_MaximumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MaximumMember" xlink:to="lab_srt_MaximumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote</link:label>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_label_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_EquityValuationAssumptionDifferenceFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:to="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_34bdf791-1a02-4156-a4c8-a622666828a9_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_FairValueLiabilityStillHeldUnrealizedGainLoss_8f9769e9-b5e0-4079-abf8-602c1f54a957_negatedLabel_en-US" xlink:label="lab_tlsi_FairValueLiabilityStillHeldUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Change in Unrealized (Gains) Losses</link:label>
    <link:label id="lab_tlsi_FairValueLiabilityStillHeldUnrealizedGainLoss_label_en-US" xlink:label="lab_tlsi_FairValueLiabilityStillHeldUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Liability, Still Held, Unrealized Gain (Loss)</link:label>
    <link:label id="lab_tlsi_FairValueLiabilityStillHeldUnrealizedGainLoss_documentation_en-US" xlink:label="lab_tlsi_FairValueLiabilityStillHeldUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Liability, Still Held, Unrealized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_FairValueLiabilityStillHeldUnrealizedGainLoss" xlink:href="tlsi-20250331.xsd#tlsi_FairValueLiabilityStillHeldUnrealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_FairValueLiabilityStillHeldUnrealizedGainLoss" xlink:to="lab_tlsi_FairValueLiabilityStillHeldUnrealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_label_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountingPoliciesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccountingPoliciesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountingPoliciesAbstract" xlink:to="lab_us-gaap_AccountingPoliciesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodSixAndThereafterMember_8ac7aac6-193c-49a9-937d-681020b88552_terseLabel_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodSixAndThereafterMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">June 30, 2026 and each Fiscal Quarter ending thereafter</link:label>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodSixAndThereafterMember_label_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodSixAndThereafterMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Feature, Period Six And Thereafter [Member]</link:label>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodSixAndThereafterMember_documentation_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodSixAndThereafterMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Feature, Period Six And Thereafter</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_RevenueBaseRedemptionFeaturePeriodSixAndThereafterMember" xlink:href="tlsi-20250331.xsd#tlsi_RevenueBaseRedemptionFeaturePeriodSixAndThereafterMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_RevenueBaseRedemptionFeaturePeriodSixAndThereafterMember" xlink:to="lab_tlsi_RevenueBaseRedemptionFeaturePeriodSixAndThereafterMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTable_16971540-65a3-4532-be67-9dbd47e368f7_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTable_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact_cfebfa98-6ff3-4695-ba7d-83278b0dd439_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Undeclared dividends on Series A preferred stock</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact_label_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock Dividends, Income Statement Impact</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockDividendsIncomeStatementImpact"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:to="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ReverseRecapitalizationLineItems_a213d593-f40c-4818-a1e9-9d7d08eba218_terseLabel_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reverse Recapitalization [Line Items]</link:label>
    <link:label id="lab_tlsi_ReverseRecapitalizationLineItems_label_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reverse Recapitalization [Line Items]</link:label>
    <link:label id="lab_tlsi_ReverseRecapitalizationLineItems_documentation_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reverse Recapitalization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ReverseRecapitalizationLineItems" xlink:href="tlsi-20250331.xsd#tlsi_ReverseRecapitalizationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ReverseRecapitalizationLineItems" xlink:to="lab_tlsi_ReverseRecapitalizationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdTradingDays_2aff0110-ced4-4d6c-b374-c8124a2c0704_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdTradingDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnout period, threshold trading days</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdTradingDays_label_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdTradingDays" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Contingent Consideration, Liability, Earnout Period, Threshold Trading Days</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdTradingDays_documentation_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdTradingDays" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Contingent Consideration, Liability, Earnout Period, Threshold Trading Days</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdTradingDays" xlink:href="tlsi-20250331.xsd#tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdTradingDays"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdTradingDays" xlink:to="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdTradingDays" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_dfac6157-7365-47bd-91f8-517af54649cd_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_CurrentFiscalYearEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CurrentFiscalYearEndDate" xlink:to="lab_dei_CurrentFiscalYearEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearNumberOfYears_3e1fa5e0-10bc-4133-a8d9-d9ab2b11f120_terseLabel_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearNumberOfYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share reserve increase, number of years</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearNumberOfYears_label_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearNumberOfYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Automatic Increase Per Year, Number of Years</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearNumberOfYears_documentation_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearNumberOfYears" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Automatic Increase Per Year, Number of Years</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearNumberOfYears" xlink:href="tlsi-20250331.xsd#tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearNumberOfYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearNumberOfYears" xlink:to="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearNumberOfYears" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_96877865-ba6b-4bb7-8579-cb61af344c8c_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoName_terseLabel_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:label id="lab_ecd_PeoName_label_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoName" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PeoName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoName" xlink:to="lab_ecd_PeoName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightOutstanding_cb25ad63-5934-42d9-8adb-4a06dfbb689c_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightOutstanding_a0ca47a5-5c8a-472f-96ee-dd0d59d12dce_periodStartLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Warrants outstanding, beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightOutstanding_5093d348-928b-47ab-85d2-2c1b5ba4a3cb_periodEndLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Warrants outstanding, ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightOutstanding_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfWarrantOrRightOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightOutstanding" xlink:to="lab_us-gaap_ClassOfWarrantOrRightOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_NonRule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:to="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_60e764e9-51f4-4223-9740-5d81c1f0b0f9_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Loss before income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod_1c708dd7-a3f5-47fc-b4ef-7e8fe3922ae3_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares purchased in ESPP offering (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Shares Issued in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_NonPeoNeoAvgTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:to="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_7967bacd-61bb-403f-bd66-f34f1fca92c5_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_AssetAcquisitionRoyaltyPercentageOverThresholdAmount_fad97ab3-7485-46ee-a615-0d0dc92619c7_terseLabel_en-US" xlink:label="lab_tlsi_AssetAcquisitionRoyaltyPercentageOverThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Royalties as a percentage of sales, over threshold amount</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionRoyaltyPercentageOverThresholdAmount_label_en-US" xlink:label="lab_tlsi_AssetAcquisitionRoyaltyPercentageOverThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Royalty Percentage, Over Threshold Amount</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionRoyaltyPercentageOverThresholdAmount_documentation_en-US" xlink:label="lab_tlsi_AssetAcquisitionRoyaltyPercentageOverThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Royalty Percentage, Over Threshold Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_AssetAcquisitionRoyaltyPercentageOverThresholdAmount" xlink:href="tlsi-20250331.xsd#tlsi_AssetAcquisitionRoyaltyPercentageOverThresholdAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_AssetAcquisitionRoyaltyPercentageOverThresholdAmount" xlink:to="lab_tlsi_AssetAcquisitionRoyaltyPercentageOverThresholdAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PreferredStockAutomaticConversionPeriod_1861a013-5190-4c03-9ea6-32d9bb69aa39_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockAutomaticConversionPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Automatic conversion, anniversary</link:label>
    <link:label id="lab_tlsi_PreferredStockAutomaticConversionPeriod_label_en-US" xlink:label="lab_tlsi_PreferredStockAutomaticConversionPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Automatic Conversion, Period</link:label>
    <link:label id="lab_tlsi_PreferredStockAutomaticConversionPeriod_documentation_en-US" xlink:label="lab_tlsi_PreferredStockAutomaticConversionPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Stock, Automatic Conversion, Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PreferredStockAutomaticConversionPeriod" xlink:href="tlsi-20250331.xsd#tlsi_PreferredStockAutomaticConversionPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PreferredStockAutomaticConversionPeriod" xlink:to="lab_tlsi_PreferredStockAutomaticConversionPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_OutstandingRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryIndName" xlink:to="lab_ecd_OutstandingRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_b8962b6e-9fad-467d-a4f4-9ffa1b02ad5d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:to="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RestatementAxis_6bce58a0-747e-4b91-b521-d9af27a01187_terseLabel_en-US" xlink:label="lab_srt_RestatementAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revision of Prior Period [Axis]</link:label>
    <link:label id="lab_srt_RestatementAxis_label_en-US" xlink:label="lab_srt_RestatementAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revision of Prior Period [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RestatementAxis" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_RestatementAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RestatementAxis" xlink:to="lab_srt_RestatementAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoMember_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO</link:label>
    <link:label id="lab_ecd_NonPeoNeoMember_label_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_NonPeoNeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoMember" xlink:to="lab_ecd_NonPeoNeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_78a533c6-ebaa-4c35-9d58-4d57cc92551c_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:to="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_AssetAcquisitionMaximumMilestoneAmount_dd90d18b-73a1-408e-8301-728cd76ce609_terseLabel_en-US" xlink:label="lab_tlsi_AssetAcquisitionMaximumMilestoneAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum aggregate milestone payments per development milestone</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionMaximumMilestoneAmount_label_en-US" xlink:label="lab_tlsi_AssetAcquisitionMaximumMilestoneAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Maximum Milestone Amount</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionMaximumMilestoneAmount_documentation_en-US" xlink:label="lab_tlsi_AssetAcquisitionMaximumMilestoneAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Maximum Milestone Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_AssetAcquisitionMaximumMilestoneAmount" xlink:href="tlsi-20250331.xsd#tlsi_AssetAcquisitionMaximumMilestoneAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_AssetAcquisitionMaximumMilestoneAmount" xlink:to="lab_tlsi_AssetAcquisitionMaximumMilestoneAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined</link:label>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_label_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgPredtrmndFlag" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AwardTmgPredtrmndFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgPredtrmndFlag" xlink:to="lab_ecd_AwardTmgPredtrmndFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_6f0bc8b9-9e68-41b0-8be7-86611548e369_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsequentEventTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeDomain" xlink:to="lab_us-gaap_SubsequentEventTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_WestminsterFacilityMember_5f538474-5a0a-41d2-bc3d-fcc2d754aa92_terseLabel_en-US" xlink:label="lab_tlsi_WestminsterFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Westminster Facility</link:label>
    <link:label id="lab_tlsi_WestminsterFacilityMember_label_en-US" xlink:label="lab_tlsi_WestminsterFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Westminster Facility [Member]</link:label>
    <link:label id="lab_tlsi_WestminsterFacilityMember_documentation_en-US" xlink:label="lab_tlsi_WestminsterFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Westminster Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_WestminsterFacilityMember" xlink:href="tlsi-20250331.xsd#tlsi_WestminsterFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_WestminsterFacilityMember" xlink:to="lab_tlsi_WestminsterFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WarrantsAndRightsNoteDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_WarrantsAndRightsNoteDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrants and Rights Note Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WarrantsAndRightsNoteDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_WarrantsAndRightsNoteDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WarrantsAndRightsNoteDisclosureAbstract" xlink:to="lab_us-gaap_WarrantsAndRightsNoteDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCashNoncurrent_fe81d4c5-96e1-4011-8dd7-23f635dcf1a9_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash (included in Other assets)</link:label>
    <link:label id="lab_us-gaap_RestrictedCashNoncurrent_label_en-US" xlink:label="lab_us-gaap_RestrictedCashNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RestrictedCashNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCashNoncurrent" xlink:to="lab_us-gaap_RestrictedCashNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_c68354b4-4175-4f1c-bbbb-cc954eedd401_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recent Accounting Pronouncements</link:label>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_SaleOfStockNotYetIssuedPricePerShare_122194b0-6d70-4b76-aa46-9b94e7c402d1_terseLabel_en-US" xlink:label="lab_tlsi_SaleOfStockNotYetIssuedPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock net yet issued, price per share (in dollars per share)</link:label>
    <link:label id="lab_tlsi_SaleOfStockNotYetIssuedPricePerShare_label_en-US" xlink:label="lab_tlsi_SaleOfStockNotYetIssuedPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale Of Stock, Not Yet Issued, Price Per Share</link:label>
    <link:label id="lab_tlsi_SaleOfStockNotYetIssuedPricePerShare_documentation_en-US" xlink:label="lab_tlsi_SaleOfStockNotYetIssuedPricePerShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sale Of Stock, Not Yet Issued, Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SaleOfStockNotYetIssuedPricePerShare" xlink:href="tlsi-20250331.xsd#tlsi_SaleOfStockNotYetIssuedPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_SaleOfStockNotYetIssuedPricePerShare" xlink:to="lab_tlsi_SaleOfStockNotYetIssuedPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_2977ea72-723c-4af9-ac82-f61eca69e59a_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net loss per common share, diluted (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EarningsPerShareDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareDiluted" xlink:to="lab_us-gaap_EarningsPerShareDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_95b103d9-94e8-4bda-bacd-dd628e8c1914_terseLabel_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_label_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementClassOfStockAxis" xlink:to="lab_us-gaap_StatementClassOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_9d24524c-b7f9-402d-afc2-87aa21cfab6e_terseLabel_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_label_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_RepurchaseAgreementCounterpartyNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:to="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock_67643476-4625-483c-8456-d8f6d099794a_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue Recognition</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RevenueFromContractWithCustomerPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_cc14fd7e-3d47-4a96-8088-766582e0eb49_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reduction in the carrying amount of right-of-use assets</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset, Periodic Reduction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureName_terseLabel_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_MeasureName_label_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureName" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_MeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureName" xlink:to="lab_ecd_MeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PrepaymentPremiumRatePeriodDomain_d8482f25-4f86-46fe-86e5-4e2c2426632c_terseLabel_en-US" xlink:label="lab_tlsi_PrepaymentPremiumRatePeriodDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepayment Premium Rate, Period [Domain]</link:label>
    <link:label id="lab_tlsi_PrepaymentPremiumRatePeriodDomain_label_en-US" xlink:label="lab_tlsi_PrepaymentPremiumRatePeriodDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepayment Premium Rate, Period [Domain]</link:label>
    <link:label id="lab_tlsi_PrepaymentPremiumRatePeriodDomain_documentation_en-US" xlink:label="lab_tlsi_PrepaymentPremiumRatePeriodDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Prepayment Premium Rate, Period [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PrepaymentPremiumRatePeriodDomain" xlink:href="tlsi-20250331.xsd#tlsi_PrepaymentPremiumRatePeriodDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PrepaymentPremiumRatePeriodDomain" xlink:to="lab_tlsi_PrepaymentPremiumRatePeriodDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_bbf67a7a-69a3-42a8-b71b-0e9711b8a00a_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_label_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityInteractiveDataCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedVacationCurrent_fa0ae724-227e-4d11-bb29-bc825bf7c9a7_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedVacationCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued vacation</link:label>
    <link:label id="lab_us-gaap_AccruedVacationCurrent_label_en-US" xlink:label="lab_us-gaap_AccruedVacationCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Vacation, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedVacationCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccruedVacationCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedVacationCurrent" xlink:to="lab_us-gaap_AccruedVacationCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_terseLabel_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement does not require Recovery</link:label>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_label_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Does Not Require Recovery [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_RestatementDoesNotRequireRecoveryTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:to="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfStockholdersEquityNoteWarrantsOrRightsTextBlock_4ed88058-30a1-4ff0-b74c-b8b4dfbe2edb_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockholdersEquityNoteWarrantsOrRightsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Warrants Outstanding</link:label>
    <link:label id="lab_us-gaap_ScheduleOfStockholdersEquityNoteWarrantsOrRightsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockholdersEquityNoteWarrantsOrRightsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Stockholders' Equity Note, Warrants or Rights [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockholdersEquityNoteWarrantsOrRightsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfStockholdersEquityNoteWarrantsOrRightsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfStockholdersEquityNoteWarrantsOrRightsTextBlock" xlink:to="lab_us-gaap_ScheduleOfStockholdersEquityNoteWarrantsOrRightsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightPercentageOfWarrantsTenderAgreement_f904090c-fd5b-4dda-9daf-33238c4f1a3b_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightPercentageOfWarrantsTenderAgreement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrant holder support for Warrant Agreement</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightPercentageOfWarrantsTenderAgreement_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightPercentageOfWarrantsTenderAgreement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Percentage of Warrants, Tender Agreement</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightPercentageOfWarrantsTenderAgreement_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightPercentageOfWarrantsTenderAgreement" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Percentage of Warrants, Tender Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightPercentageOfWarrantsTenderAgreement" xlink:href="tlsi-20250331.xsd#tlsi_ClassOfWarrantOrRightPercentageOfWarrantsTenderAgreement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightPercentageOfWarrantsTenderAgreement" xlink:to="lab_tlsi_ClassOfWarrantOrRightPercentageOfWarrantsTenderAgreement" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeatureAmount_d63052e3-a972-4f99-9990-a39a1069a736_terseLabel_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeatureAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue base redemption feature, amount</link:label>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeatureAmount_d4d0781e-3cf4-4c67-89f3-0569dbc2a3dd_negatedTerseLabel_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeatureAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Revenue base redemption liability</link:label>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeatureAmount_label_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeatureAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Feature, Amount</link:label>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeatureAmount_documentation_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeatureAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Feature, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_RevenueBaseRedemptionFeatureAmount" xlink:href="tlsi-20250331.xsd#tlsi_RevenueBaseRedemptionFeatureAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_RevenueBaseRedemptionFeatureAmount" xlink:to="lab_tlsi_RevenueBaseRedemptionFeatureAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_e6db3d80-3b18-4491-bcfb-d95c6c7069f4_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesIssued" xlink:to="lab_us-gaap_PreferredStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems_5d72a96d-fd9d-4919-b63b-ab6bb2a1f974_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements or Change in Accounting Principle [Line Items]</link:label>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems_label_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements or Change in Accounting Principle [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:to="lab_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:to="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationLiabilityMeasurementInput_60dbad04-cabb-48ea-94e1-bbe93fcb85ea_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationLiabilityMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contingent earnout liability, measurement input</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationLiabilityMeasurementInput_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationLiabilityMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Contingent Consideration, Liability, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationContingentConsiderationLiabilityMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationContingentConsiderationLiabilityMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationContingentConsiderationLiabilityMeasurementInput" xlink:to="lab_us-gaap_BusinessCombinationContingentConsiderationLiabilityMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensation_bcfccc1e-855b-4b34-8121-62953438e30a_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock-based compensation expense</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Noncash Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensation" xlink:to="lab_us-gaap_ShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SellingAndMarketingExpense_cbf6ecd8-23ea-458c-8ff5-c48719b6aa27_terseLabel_en-US" xlink:label="lab_us-gaap_SellingAndMarketingExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sales and marketing</link:label>
    <link:label id="lab_us-gaap_SellingAndMarketingExpense_label_en-US" xlink:label="lab_us-gaap_SellingAndMarketingExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Selling and Marketing Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SellingAndMarketingExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SellingAndMarketingExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SellingAndMarketingExpense" xlink:to="lab_us-gaap_SellingAndMarketingExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_FairValueMeasurementReconciliationLiabilityPurchasesSalesIssuancesSettlements_1fcb5373-da85-4871-b57e-e771127198d7_terseLabel_en-US" xlink:label="lab_tlsi_FairValueMeasurementReconciliationLiabilityPurchasesSalesIssuancesSettlements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuances (Settlements)</link:label>
    <link:label id="lab_tlsi_FairValueMeasurementReconciliationLiabilityPurchasesSalesIssuancesSettlements_label_en-US" xlink:label="lab_tlsi_FairValueMeasurementReconciliationLiabilityPurchasesSalesIssuancesSettlements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement Reconciliation, Liability, Purchases, (Sales), Issuances, (Settlements)</link:label>
    <link:label id="lab_tlsi_FairValueMeasurementReconciliationLiabilityPurchasesSalesIssuancesSettlements_documentation_en-US" xlink:label="lab_tlsi_FairValueMeasurementReconciliationLiabilityPurchasesSalesIssuancesSettlements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement Reconciliation, Liability, Purchases, (Sales), Issuances, (Settlements)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_FairValueMeasurementReconciliationLiabilityPurchasesSalesIssuancesSettlements" xlink:href="tlsi-20250331.xsd#tlsi_FairValueMeasurementReconciliationLiabilityPurchasesSalesIssuancesSettlements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_FairValueMeasurementReconciliationLiabilityPurchasesSalesIssuancesSettlements" xlink:to="lab_tlsi_FairValueMeasurementReconciliationLiabilityPurchasesSalesIssuancesSettlements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment_60d856c1-463b-4492-b44d-981c8df5d488_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from the disposal of property and equipment</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:to="lab_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DynavaxTechnologiesMember_cf298bfd-dbc8-4e16-8f75-587e13ae998c_terseLabel_en-US" xlink:label="lab_tlsi_DynavaxTechnologiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dynavax Technologies</link:label>
    <link:label id="lab_tlsi_DynavaxTechnologiesMember_label_en-US" xlink:label="lab_tlsi_DynavaxTechnologiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dynavax Technologies [Member]</link:label>
    <link:label id="lab_tlsi_DynavaxTechnologiesMember_documentation_en-US" xlink:label="lab_tlsi_DynavaxTechnologiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Dynavax Technologies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DynavaxTechnologiesMember" xlink:href="tlsi-20250331.xsd#tlsi_DynavaxTechnologiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DynavaxTechnologiesMember" xlink:to="lab_tlsi_DynavaxTechnologiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_104cc4fb-5643-4588-8c24-f051975cf8a5_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Income tax expense</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementSEPADerivativeLiabilityMember_ded43316-3423-49ae-b40e-928c7593e198_terseLabel_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementSEPADerivativeLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SEPA derivative liability</link:label>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementSEPADerivativeLiabilityMember_label_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementSEPADerivativeLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Standby Equity Purchase Agreement (SEPA) Derivative Liability [Member]</link:label>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementSEPADerivativeLiabilityMember_documentation_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementSEPADerivativeLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Standby Equity Purchase Agreement (SEPA) Derivative Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_StandbyEquityPurchaseAgreementSEPADerivativeLiabilityMember" xlink:href="tlsi-20250331.xsd#tlsi_StandbyEquityPurchaseAgreementSEPADerivativeLiabilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_StandbyEquityPurchaseAgreementSEPADerivativeLiabilityMember" xlink:to="lab_tlsi_StandbyEquityPurchaseAgreementSEPADerivativeLiabilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward_916b06c4-762c-4b19-b192-75088b43b9f8_terseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward_label_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward" xlink:to="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_WarrantLiability_76e18a97-38af-4253-8e66-1799f7836f43_negatedTerseLabel_en-US" xlink:label="lab_tlsi_WarrantLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Warrant liability</link:label>
    <link:label id="lab_tlsi_WarrantLiability_label_en-US" xlink:label="lab_tlsi_WarrantLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrant Liability</link:label>
    <link:label id="lab_tlsi_WarrantLiability_documentation_en-US" xlink:label="lab_tlsi_WarrantLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Warrant Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_WarrantLiability" xlink:href="tlsi-20250331.xsd#tlsi_WarrantLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_WarrantLiability" xlink:to="lab_tlsi_WarrantLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_b937069c-2400-44e0-b9fc-9393cf533576_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecognized compensation expense, recognition period</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:to="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_5f4a5fa8-abcb-4ae5-8b3e-28ca2ddd35e8_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer, Excluding Assessed Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockDividendRatePercentage_ec9294a2-8174-49d1-a267-5c307bc80b1a_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, dividend rate, percentage</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendRatePercentage_label_en-US" xlink:label="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Dividend Rate, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockDividendRatePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockDividendRatePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockDividendRatePercentage" xlink:to="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_AdditionalPaidInCapital_0851259c-3dc1-4e69-b4ed-d857925b0cea_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid-in capital</link:label>
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    <link:label id="lab_tlsi_FairValueLiabilitiesMeasurementReconciliationCalculationRollForward_label_en-US" xlink:label="lab_tlsi_FairValueLiabilitiesMeasurementReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Liabilities Measurement Reconciliation, Calculation [Roll Forward]</link:label>
    <link:label id="lab_tlsi_FairValueLiabilitiesMeasurementReconciliationCalculationRollForward_documentation_en-US" xlink:label="lab_tlsi_FairValueLiabilitiesMeasurementReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Liabilities Measurement Reconciliation, Calculation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_FairValueLiabilitiesMeasurementReconciliationCalculationRollForward" xlink:href="tlsi-20250331.xsd#tlsi_FairValueLiabilitiesMeasurementReconciliationCalculationRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_FairValueLiabilitiesMeasurementReconciliationCalculationRollForward" xlink:to="lab_tlsi_FairValueLiabilitiesMeasurementReconciliationCalculationRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_ebc72b7d-c5af-4516-bbd4-d84ab552437d_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MeasurementInputTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputTypeAxis" xlink:to="lab_us-gaap_MeasurementInputTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_IndividualAxis_terseLabel_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individual:</link:label>
    <link:label id="lab_ecd_IndividualAxis_label_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Individual [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_IndividualAxis" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_IndividualAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_IndividualAxis" xlink:to="lab_ecd_IndividualAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryNet_caf900bf-ad41-4fcc-8395-44c1c7963a89_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Inventory, net</link:label>
    <link:label id="lab_us-gaap_InventoryNet_7546b4d3-9f24-4dcd-8e15-bea74d51e25c_totalLabel_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Inventory, net</link:label>
    <link:label id="lab_us-gaap_InventoryNet_label_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryNet" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InventoryNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryNet" xlink:to="lab_us-gaap_InventoryNet" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodAxis_c4f3cc68-53ec-4a9b-a079-18d5b188157e_terseLabel_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Feature, Period [Axis]</link:label>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodAxis_label_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Feature, Period [Axis]</link:label>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodAxis_documentation_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Feature, Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_RevenueBaseRedemptionFeaturePeriodAxis" xlink:href="tlsi-20250331.xsd#tlsi_RevenueBaseRedemptionFeaturePeriodAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_RevenueBaseRedemptionFeaturePeriodAxis" xlink:to="lab_tlsi_RevenueBaseRedemptionFeaturePeriodAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightRollForward_23abc054-8b11-4c47-ae52-589b5ccec51f_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Roll Forward]</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightRollForward_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right [Roll Forward]</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightRollForward_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightRollForward" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightRollForward" xlink:href="tlsi-20250331.xsd#tlsi_ClassOfWarrantOrRightRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightRollForward" xlink:to="lab_tlsi_ClassOfWarrantOrRightRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_4792b39a-3d42-40b1-8c67-bcc9041cf227_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeDomain" xlink:to="lab_us-gaap_LongtermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_1288fe82-0416-4ff3-adde-e4784188e203_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityAddressStateOrProvince"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementLineItems_7ef58d96-daf0-4bc8-ae8d-c7cc16dcf5d5_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputTypeDomain_8ae5afb1-0c12-47fd-881d-56289d913be8_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Domain]</link:label>
    <link:label id="lab_us-gaap_MeasurementInputTypeDomain_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MeasurementInputTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputTypeDomain" xlink:to="lab_us-gaap_MeasurementInputTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:to="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis</link:label>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_label_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompAnalysisTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_ErrCompAnalysisTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompAnalysisTextBlock" xlink:to="lab_ecd_ErrCompAnalysisTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableTradeCurrent_5c3389b1-4984-452f-b6ff-9107f60f81d4_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableTradeCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trade payables</link:label>
    <link:label id="lab_us-gaap_AccountsPayableTradeCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsPayableTradeCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable, Trade, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableTradeCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccountsPayableTradeCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableTradeCurrent" xlink:to="lab_us-gaap_AccountsPayableTradeCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_48ba0733-bba7-4d4f-907f-f1fb9cec7185_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating expenses:</link:label>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpensesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpensesAbstract" xlink:to="lab_us-gaap_OperatingExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_WarrantLiabilityMeasurementInput_8137ab72-3dfc-4de3-8cc3-274ae582d072_terseLabel_en-US" xlink:label="lab_tlsi_WarrantLiabilityMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative liability, measurement input</link:label>
    <link:label id="lab_tlsi_WarrantLiabilityMeasurementInput_label_en-US" xlink:label="lab_tlsi_WarrantLiabilityMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrant Liability, Measurement Input</link:label>
    <link:label id="lab_tlsi_WarrantLiabilityMeasurementInput_documentation_en-US" xlink:label="lab_tlsi_WarrantLiabilityMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Warrant Liability, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_WarrantLiabilityMeasurementInput" xlink:href="tlsi-20250331.xsd#tlsi_WarrantLiabilityMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_WarrantLiabilityMeasurementInput" xlink:to="lab_tlsi_WarrantLiabilityMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementTerm_8d796f19-9a92-4b6a-9561-80dc488d7912_terseLabel_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchase agreement period</link:label>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementTerm_label_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Standby Equity Purchase Agreement, Term</link:label>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementTerm_documentation_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Standby Equity Purchase Agreement, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_StandbyEquityPurchaseAgreementTerm" xlink:href="tlsi-20250331.xsd#tlsi_StandbyEquityPurchaseAgreementTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_StandbyEquityPurchaseAgreementTerm" xlink:to="lab_tlsi_StandbyEquityPurchaseAgreementTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_AllianceProgramTerm_b9f61370-bd5b-4fe4-b06a-0b3d4972c185_terseLabel_en-US" xlink:label="lab_tlsi_AllianceProgramTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Alliance program, term</link:label>
    <link:label id="lab_tlsi_AllianceProgramTerm_label_en-US" xlink:label="lab_tlsi_AllianceProgramTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Alliance Program, Term</link:label>
    <link:label id="lab_tlsi_AllianceProgramTerm_documentation_en-US" xlink:label="lab_tlsi_AllianceProgramTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Alliance Program, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_AllianceProgramTerm" xlink:href="tlsi-20250331.xsd#tlsi_AllianceProgramTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_AllianceProgramTerm" xlink:to="lab_tlsi_AllianceProgramTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_be315c9b-2366-4bb0-a4d0-55bb289c871d_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities and Stockholders&#8217; Deficit</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPaidCapitalized_eef95cc3-beda-43b5-a412-e7b747d1f720_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaidCapitalized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash paid for interest expense</link:label>
    <link:label id="lab_us-gaap_InterestPaidCapitalized_label_en-US" xlink:label="lab_us-gaap_InterestPaidCapitalized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Paid, Capitalized, Investing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPaidCapitalized" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InterestPaidCapitalized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPaidCapitalized" xlink:to="lab_us-gaap_InterestPaidCapitalized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_1a5e73da-26ef-4c13-9010-0696866daed6_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SEPA derivative liability</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_d3a53fd2-01e4-4d2f-bc09-248e8bc80f29_periodStartLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_0beddb5d-803a-4efa-a12e-3c7f66739a9d_periodEndLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_MeasurementInputExpectedDrawsMember_5abb36ca-606c-4a35-83df-ea5fd124f54d_terseLabel_en-US" xlink:label="lab_tlsi_MeasurementInputExpectedDrawsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expected draws</link:label>
    <link:label id="lab_tlsi_MeasurementInputExpectedDrawsMember_label_en-US" xlink:label="lab_tlsi_MeasurementInputExpectedDrawsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Expected Draws [Member]</link:label>
    <link:label id="lab_tlsi_MeasurementInputExpectedDrawsMember_documentation_en-US" xlink:label="lab_tlsi_MeasurementInputExpectedDrawsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Expected Draws</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_MeasurementInputExpectedDrawsMember" xlink:href="tlsi-20250331.xsd#tlsi_MeasurementInputExpectedDrawsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_MeasurementInputExpectedDrawsMember" xlink:to="lab_tlsi_MeasurementInputExpectedDrawsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfErrorCorrectionsAndPriorPeriodAdjustmentsTextBlock_9ce2fde5-ddaa-4e6f-a324-949013ab178c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfErrorCorrectionsAndPriorPeriodAdjustmentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Error Corrections and Prior Period Adjustments</link:label>
    <link:label id="lab_us-gaap_ScheduleOfErrorCorrectionsAndPriorPeriodAdjustmentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfErrorCorrectionsAndPriorPeriodAdjustmentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Error Corrections and Prior Period Adjustments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfErrorCorrectionsAndPriorPeriodAdjustmentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfErrorCorrectionsAndPriorPeriodAdjustmentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfErrorCorrectionsAndPriorPeriodAdjustmentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfErrorCorrectionsAndPriorPeriodAdjustmentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativesPolicyTextBlock_7c1233be-005e-4d9b-84c8-7c7c5fcea65c_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Standby Equity Purchase Agreement</link:label>
    <link:label id="lab_us-gaap_DerivativesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_DerivativesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivatives, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativesPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativesPolicyTextBlock" xlink:to="lab_us-gaap_DerivativesPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MinimumMember_00f5e17b-440d-4cde-975d-68132913385a_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum</link:label>
    <link:label id="lab_srt_MinimumMember_label_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Minimum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_MinimumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MinimumMember" xlink:to="lab_srt_MinimumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDeterminationDate_terseLabel_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:label id="lab_ecd_RestatementDeterminationDate_label_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDeterminationDate" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_RestatementDeterminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDeterminationDate" xlink:to="lab_ecd_RestatementDeterminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrAdoptionDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adoption Date</link:label>
    <link:label id="lab_ecd_TrdArrAdoptionDate_label_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Adoption Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrAdoptionDate" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_TrdArrAdoptionDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrAdoptionDate" xlink:to="lab_ecd_TrdArrAdoptionDate" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTable_terseLabel_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure</link:label>
    <link:label id="lab_ecd_PvpTable_label_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTable" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PvpTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTable" xlink:to="lab_ecd_PvpTable" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_NumberOfEquityIncentivePlans_6e866f28-a160-464c-8669-20bb8880de3a_terseLabel_en-US" xlink:label="lab_tlsi_NumberOfEquityIncentivePlans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of equity incentive plans</link:label>
    <link:label id="lab_tlsi_NumberOfEquityIncentivePlans_label_en-US" xlink:label="lab_tlsi_NumberOfEquityIncentivePlans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Equity Incentive Plans</link:label>
    <link:label id="lab_tlsi_NumberOfEquityIncentivePlans_documentation_en-US" xlink:label="lab_tlsi_NumberOfEquityIncentivePlans" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Equity Incentive Plans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_NumberOfEquityIncentivePlans" xlink:href="tlsi-20250331.xsd#tlsi_NumberOfEquityIncentivePlans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_NumberOfEquityIncentivePlans" xlink:to="lab_tlsi_NumberOfEquityIncentivePlans" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_b0aff535-4940-4c1c-86b0-c41f0787b3b8_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Right-of-use assets</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompRecoveryTable_terseLabel_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery</link:label>
    <link:label id="lab_ecd_ErrCompRecoveryTable_label_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompRecoveryTable" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_ErrCompRecoveryTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompRecoveryTable" xlink:to="lab_ecd_ErrCompRecoveryTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossLineItems_ab11175c-4a4f-4e57-ae18-f9fa8407c5bf_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativeInstrumentsGainLossLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:to="lab_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_078c9fd0-e2a5-4850-9a0e-701538c4e8fe_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock options outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProvisionForDoubtfulAccounts_24d18d68-6fed-4114-b83b-f097670b4d41_terseLabel_en-US" xlink:label="lab_us-gaap_ProvisionForDoubtfulAccounts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amount charged (recovered) to costs and expenses</link:label>
    <link:label id="lab_us-gaap_ProvisionForDoubtfulAccounts_b0c683c6-83c9-45d2-9545-cfaf4dd671b1_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ProvisionForDoubtfulAccounts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Amount charged (recovered) to costs and expenses</link:label>
    <link:label id="lab_us-gaap_ProvisionForDoubtfulAccounts_label_en-US" xlink:label="lab_us-gaap_ProvisionForDoubtfulAccounts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Credit Loss Expense (Reversal)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProvisionForDoubtfulAccounts" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ProvisionForDoubtfulAccounts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProvisionForDoubtfulAccounts" xlink:to="lab_us-gaap_ProvisionForDoubtfulAccounts" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year</link:label>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:to="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock_74cceae6-266f-4075-b6f4-62a0a06ae3e6_terseLabel_en-US" xlink:label="lab_us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Plan Balances</link:label>
    <link:label id="lab_us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock_label_en-US" xlink:label="lab_us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disclosure of Share-Based Compensation Arrangements by Share-Based Payment Award [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock" xlink:to="lab_us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationSecondReset_6c322f50-5acb-48e1-94d7-cd245cb28067_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationSecondReset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion price, second automatic reset</link:label>
    <link:label id="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationSecondReset_label_en-US" xlink:label="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationSecondReset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Conversion Price, Automatic Reset Duration, Second Reset</link:label>
    <link:label id="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationSecondReset_documentation_en-US" xlink:label="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationSecondReset" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Stock, Conversion Price, Automatic Reset Duration, Second Reset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PreferredStockConversionPriceAutomaticResetDurationSecondReset" xlink:href="tlsi-20250331.xsd#tlsi_PreferredStockConversionPriceAutomaticResetDurationSecondReset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PreferredStockConversionPriceAutomaticResetDurationSecondReset" xlink:to="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationSecondReset" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodVestingPercentage_d133fca6-7e9b-44f2-aa7b-802f4d4d5cf8_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodVestingPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnout shares vesting percentage</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodVestingPercentage_label_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodVestingPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Contingent Consideration, Liability, Earnout Period, Vesting Percentage</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodVestingPercentage_documentation_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodVestingPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Contingent Consideration, Liability, Earnout Period, Vesting Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodVestingPercentage" xlink:href="tlsi-20250331.xsd#tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodVestingPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodVestingPercentage" xlink:to="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodVestingPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityByClassOfStockTable_81f44873-896c-414a-a4c6-50a2a9e8b757_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityByClassOfStockTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temporary Equity, by Class of Stock [Table]</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityByClassOfStockTable_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityByClassOfStockTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, by Class of Stock [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityByClassOfStockTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TemporaryEquityByClassOfStockTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityByClassOfStockTable" xlink:to="lab_us-gaap_TemporaryEquityByClassOfStockTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardExrcPrice_terseLabel_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise Price</link:label>
    <link:label id="lab_ecd_AwardExrcPrice_label_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardExrcPrice" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AwardExrcPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardExrcPrice" xlink:to="lab_ecd_AwardExrcPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseContractualTermAxis_26e5d301-f97b-4245-99af-642dd85209a1_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseContractualTermAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease Contractual Term [Axis]</link:label>
    <link:label id="lab_us-gaap_LeaseContractualTermAxis_label_en-US" xlink:label="lab_us-gaap_LeaseContractualTermAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease Contractual Term [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseContractualTermAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LeaseContractualTermAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseContractualTermAxis" xlink:to="lab_us-gaap_LeaseContractualTermAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockCapitalSharesReservedForFutureIssuance_87852cc8-b057-4141-b937-d65400054501_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockCapitalSharesReservedForFutureIssuance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock available for future issuance (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockCapitalSharesReservedForFutureIssuance_label_en-US" xlink:label="lab_us-gaap_PreferredStockCapitalSharesReservedForFutureIssuance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Capital Shares Reserved for Future Issuance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockCapitalSharesReservedForFutureIssuance" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockCapitalSharesReservedForFutureIssuance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockCapitalSharesReservedForFutureIssuance" xlink:to="lab_us-gaap_PreferredStockCapitalSharesReservedForFutureIssuance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockTextBlock_aa73125a-6d4a-4ab8-a75b-56565ef3de1b_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Convertible Preferred Stock</link:label>
    <link:label id="lab_us-gaap_PreferredStockTextBlock_label_en-US" xlink:label="lab_us-gaap_PreferredStockTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockTextBlock" xlink:to="lab_us-gaap_PreferredStockTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionTable_41f7944c-74cb-4ca3-888a-ece8dad2f529_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Table]</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionTable_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AssetAcquisitionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionTable" xlink:to="lab_us-gaap_AssetAcquisitionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_RevenueRecognitionRebatesRecognized_496bce1e-5152-4978-8556-bba6e504f896_terseLabel_en-US" xlink:label="lab_tlsi_RevenueRecognitionRebatesRecognized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue recognition, rebates recognized</link:label>
    <link:label id="lab_tlsi_RevenueRecognitionRebatesRecognized_label_en-US" xlink:label="lab_tlsi_RevenueRecognitionRebatesRecognized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue Recognition, Rebates Recognized</link:label>
    <link:label id="lab_tlsi_RevenueRecognitionRebatesRecognized_documentation_en-US" xlink:label="lab_tlsi_RevenueRecognitionRebatesRecognized" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Revenue Recognition, Rebates Recognized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_RevenueRecognitionRebatesRecognized" xlink:href="tlsi-20250331.xsd#tlsi_RevenueRecognitionRebatesRecognized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_RevenueRecognitionRebatesRecognized" xlink:to="lab_tlsi_RevenueRecognitionRebatesRecognized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_7c4a854d-d0a6-4a74-a355-96aa2a84fb47_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Loss Per Share</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EarningsPerShareTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareTextBlock" xlink:to="lab_us-gaap_EarningsPerShareTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrDuration_terseLabel_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arrangement Duration</link:label>
    <link:label id="lab_ecd_TrdArrDuration_label_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Duration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrDuration" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_TrdArrDuration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrDuration" xlink:to="lab_ecd_TrdArrDuration" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RevisionOfPriorPeriodErrorCorrectionAdjustmentMember_ba3a74b5-0f26-4d6d-a199-49c3d76f2d74_terseLabel_en-US" xlink:label="lab_srt_RevisionOfPriorPeriodErrorCorrectionAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revision of Prior Period, Error Correction, Adjustment</link:label>
    <link:label id="lab_srt_RevisionOfPriorPeriodErrorCorrectionAdjustmentMember_label_en-US" xlink:label="lab_srt_RevisionOfPriorPeriodErrorCorrectionAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revision of Prior Period, Error Correction, Adjustment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RevisionOfPriorPeriodErrorCorrectionAdjustmentMember" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_RevisionOfPriorPeriodErrorCorrectionAdjustmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RevisionOfPriorPeriodErrorCorrectionAdjustmentMember" xlink:to="lab_srt_RevisionOfPriorPeriodErrorCorrectionAdjustmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventMember_c0a562b5-928e-4a64-9832-b4742d4268a6_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event</link:label>
    <link:label id="lab_us-gaap_SubsequentEventMember_label_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsequentEventMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventMember" xlink:to="lab_us-gaap_SubsequentEventMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeFinanceLeasesTextBlock_2f678b34-3089-4d26-9e79-4a46dda2de23_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeFinanceLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases</link:label>
    <link:label id="lab_us-gaap_LesseeFinanceLeasesTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeFinanceLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Finance Leases [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeFinanceLeasesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeFinanceLeasesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeFinanceLeasesTextBlock" xlink:to="lab_us-gaap_LesseeFinanceLeasesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_3a45a2de-beee-474d-a711-6c1dda496b06_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise of options</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Stock Options Exercised</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_WorkingCapitalWarrantsMember_c8198565-eb76-4fcb-befc-84e4262aadf1_terseLabel_en-US" xlink:label="lab_tlsi_WorkingCapitalWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Working capital warrants</link:label>
    <link:label id="lab_tlsi_WorkingCapitalWarrantsMember_9bcd1bc9-1ef3-46a5-b725-83f1bab4cbb7_verboseLabel_en-US" xlink:label="lab_tlsi_WorkingCapitalWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Working Capital Warrants</link:label>
    <link:label id="lab_tlsi_WorkingCapitalWarrantsMember_label_en-US" xlink:label="lab_tlsi_WorkingCapitalWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Working Capital Warrants [Member]</link:label>
    <link:label id="lab_tlsi_WorkingCapitalWarrantsMember_documentation_en-US" xlink:label="lab_tlsi_WorkingCapitalWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Working Capital Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_WorkingCapitalWarrantsMember" xlink:href="tlsi-20250331.xsd#tlsi_WorkingCapitalWarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_WorkingCapitalWarrantsMember" xlink:to="lab_tlsi_WorkingCapitalWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_b17cb6f0-0ac6-492d-a9f5-f8e5bfe60b46_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">RSU weighted average fair value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxPolicyTextBlock_241a4e32-1aff-4eaf-b2b7-8215dde6079d_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeTaxPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxPolicyTextBlock" xlink:to="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote</link:label>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_label_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PeerGroupIssuersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:to="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_InitialOrbiMedWarrantSubstituteWarrantCertificateNumberTwoMember_3cf8044d-b9f9-4f7f-8302-6eed1779e8fe_terseLabel_en-US" xlink:label="lab_tlsi_InitialOrbiMedWarrantSubstituteWarrantCertificateNumberTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Initial OrbiMed Warrant, Substitute Warrant Certificate Number Two</link:label>
    <link:label id="lab_tlsi_InitialOrbiMedWarrantSubstituteWarrantCertificateNumberTwoMember_label_en-US" xlink:label="lab_tlsi_InitialOrbiMedWarrantSubstituteWarrantCertificateNumberTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Initial OrbiMed Warrant, Substitute Warrant Certificate Number Two [Member]</link:label>
    <link:label id="lab_tlsi_InitialOrbiMedWarrantSubstituteWarrantCertificateNumberTwoMember_documentation_en-US" xlink:label="lab_tlsi_InitialOrbiMedWarrantSubstituteWarrantCertificateNumberTwoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Initial OrbiMed Warrant, Substitute Warrant Certificate Number Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_InitialOrbiMedWarrantSubstituteWarrantCertificateNumberTwoMember" xlink:href="tlsi-20250331.xsd#tlsi_InitialOrbiMedWarrantSubstituteWarrantCertificateNumberTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_InitialOrbiMedWarrantSubstituteWarrantCertificateNumberTwoMember" xlink:to="lab_tlsi_InitialOrbiMedWarrantSubstituteWarrantCertificateNumberTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePercentageOfInitialShareReserve_ae005774-08dd-4a6e-adc5-d979a75c840a_terseLabel_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePercentageOfInitialShareReserve" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation arrangement by share-based payment award, automatic increase, percentage of initial share reserve</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePercentageOfInitialShareReserve_label_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePercentageOfInitialShareReserve" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement By Share-based Payment Award, Automatic Increase, Percentage of Initial Share Reserve</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePercentageOfInitialShareReserve_documentation_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePercentageOfInitialShareReserve" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement By Share-based Payment Award, Automatic Increase, Percentage of Initial Share Reserve</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePercentageOfInitialShareReserve" xlink:href="tlsi-20250331.xsd#tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePercentageOfInitialShareReserve"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePercentageOfInitialShareReserve" xlink:to="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePercentageOfInitialShareReserve" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_terseLabel_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement</link:label>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_label_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_MtrlTermsOfTrdArrTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:to="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodDomain_0bd493de-30a8-435e-9e23-146ee2f09078_terseLabel_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Feature, Period [Domain]</link:label>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodDomain_label_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Feature, Period [Domain]</link:label>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodDomain_documentation_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Feature, Period [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_RevenueBaseRedemptionFeaturePeriodDomain" xlink:href="tlsi-20250331.xsd#tlsi_RevenueBaseRedemptionFeaturePeriodDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_RevenueBaseRedemptionFeaturePeriodDomain" xlink:to="lab_tlsi_RevenueBaseRedemptionFeaturePeriodDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_OrbiMedWarrantsMember_fce0ebbe-c4fa-4043-8661-4e45c1c9995e_terseLabel_en-US" xlink:label="lab_tlsi_OrbiMedWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">OrbiMed Warrants liability</link:label>
    <link:label id="lab_tlsi_OrbiMedWarrantsMember_e8888014-680f-44a7-bcec-de81ad4f7560_verboseLabel_en-US" xlink:label="lab_tlsi_OrbiMedWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">OrbiMed Warrants</link:label>
    <link:label id="lab_tlsi_OrbiMedWarrantsMember_label_en-US" xlink:label="lab_tlsi_OrbiMedWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OrbiMed Warrants [Member]</link:label>
    <link:label id="lab_tlsi_OrbiMedWarrantsMember_documentation_en-US" xlink:label="lab_tlsi_OrbiMedWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">OrbiMed Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_OrbiMedWarrantsMember" xlink:href="tlsi-20250331.xsd#tlsi_OrbiMedWarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_OrbiMedWarrantsMember" xlink:to="lab_tlsi_OrbiMedWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllIndividualsMember_terseLabel_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Individuals</link:label>
    <link:label id="lab_ecd_AllIndividualsMember_label_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Individuals [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllIndividualsMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AllIndividualsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="lab_ecd_AllIndividualsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesOutstanding_0e3711fc-56d7-47fc-b418-6f57b64d2bc5_terseLabel_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding (in shares)</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesOutstanding_label_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Outstanding</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesOutstanding_documentation_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesOutstanding" xlink:href="tlsi-20250331.xsd#tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesOutstanding" xlink:to="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoMember_terseLabel_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO</link:label>
    <link:label id="lab_ecd_PeoMember_label_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoMember" xlink:to="lab_ecd_PeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityLineItems_137ee6c9-622c-4146-b9af-d14a187736c3_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temporary Equity [Line Items]</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityLineItems_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TemporaryEquityLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityLineItems" xlink:to="lab_us-gaap_TemporaryEquityLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_InitialOrbiMedWarrantMember_353418fe-f04a-4519-9a00-63a0bcc8642a_terseLabel_en-US" xlink:label="lab_tlsi_InitialOrbiMedWarrantMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Initial OrbiMed Warrant</link:label>
    <link:label id="lab_tlsi_InitialOrbiMedWarrantMember_label_en-US" xlink:label="lab_tlsi_InitialOrbiMedWarrantMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Initial OrbiMed Warrant [Member]</link:label>
    <link:label id="lab_tlsi_InitialOrbiMedWarrantMember_documentation_en-US" xlink:label="lab_tlsi_InitialOrbiMedWarrantMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Initial OrbiMed Warrant</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_InitialOrbiMedWarrantMember" xlink:href="tlsi-20250331.xsd#tlsi_InitialOrbiMedWarrantMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_InitialOrbiMedWarrantMember" xlink:to="lab_tlsi_InitialOrbiMedWarrantMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeTaxDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:to="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndName_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_TrdArrIndName_label_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndName" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_TrdArrIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndName" xlink:to="lab_ecd_TrdArrIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_AssetAcquisitionRoyaltiesSalesThresholdAmount_a5d9cfab-952a-461b-af63-4cd7a36c959d_terseLabel_en-US" xlink:label="lab_tlsi_AssetAcquisitionRoyaltiesSalesThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Royalties, sales threshold amount</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionRoyaltiesSalesThresholdAmount_label_en-US" xlink:label="lab_tlsi_AssetAcquisitionRoyaltiesSalesThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Royalties, Sales Threshold Amount</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionRoyaltiesSalesThresholdAmount_documentation_en-US" xlink:label="lab_tlsi_AssetAcquisitionRoyaltiesSalesThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Royalties, Sales Threshold Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_AssetAcquisitionRoyaltiesSalesThresholdAmount" xlink:href="tlsi-20250331.xsd#tlsi_AssetAcquisitionRoyaltiesSalesThresholdAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_AssetAcquisitionRoyaltiesSalesThresholdAmount" xlink:to="lab_tlsi_AssetAcquisitionRoyaltiesSalesThresholdAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_185fde4d-e3e7-4a1e-b288-19c8e4a837b9_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other expense, net</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Nonoperating Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherNonoperatingIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:to="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_LesseeOperatingLeaseNumberOfRenewalOptions_f6fe64dd-4479-4bf2-8012-26a92db2dd9d_terseLabel_en-US" xlink:label="lab_tlsi_LesseeOperatingLeaseNumberOfRenewalOptions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of lease renewal options</link:label>
    <link:label id="lab_tlsi_LesseeOperatingLeaseNumberOfRenewalOptions_label_en-US" xlink:label="lab_tlsi_LesseeOperatingLeaseNumberOfRenewalOptions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Number Of Renewal Options</link:label>
    <link:label id="lab_tlsi_LesseeOperatingLeaseNumberOfRenewalOptions_documentation_en-US" xlink:label="lab_tlsi_LesseeOperatingLeaseNumberOfRenewalOptions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Number Of Renewal Options</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_LesseeOperatingLeaseNumberOfRenewalOptions" xlink:href="tlsi-20250331.xsd#tlsi_LesseeOperatingLeaseNumberOfRenewalOptions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_LesseeOperatingLeaseNumberOfRenewalOptions" xlink:to="lab_tlsi_LesseeOperatingLeaseNumberOfRenewalOptions" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_NoncashInterestExpense_6a7b034b-990f-4fa1-9a42-deb66c3eaa58_terseLabel_en-US" xlink:label="lab_tlsi_NoncashInterestExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-cash interest expense</link:label>
    <link:label id="lab_tlsi_NoncashInterestExpense_label_en-US" xlink:label="lab_tlsi_NoncashInterestExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncash Interest Expense</link:label>
    <link:label id="lab_tlsi_NoncashInterestExpense_documentation_en-US" xlink:label="lab_tlsi_NoncashInterestExpense" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Noncash Interest Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_NoncashInterestExpense" xlink:href="tlsi-20250331.xsd#tlsi_NoncashInterestExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_NoncashInterestExpense" xlink:to="lab_tlsi_NoncashInterestExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_CommonStockSharePriceMarketPriceNumberOfConsecutiveTradingDays_1f58b143-4e10-4a67-9c16-824f4652692b_terseLabel_en-US" xlink:label="lab_tlsi_CommonStockSharePriceMarketPriceNumberOfConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchase agreement, number of trading days used for measurement of market price</link:label>
    <link:label id="lab_tlsi_CommonStockSharePriceMarketPriceNumberOfConsecutiveTradingDays_label_en-US" xlink:label="lab_tlsi_CommonStockSharePriceMarketPriceNumberOfConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Share Price, Market Price, Number Of Consecutive Trading Days</link:label>
    <link:label id="lab_tlsi_CommonStockSharePriceMarketPriceNumberOfConsecutiveTradingDays_documentation_en-US" xlink:label="lab_tlsi_CommonStockSharePriceMarketPriceNumberOfConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock, Share Price, Market Price, Number Of Consecutive Trading Days</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_CommonStockSharePriceMarketPriceNumberOfConsecutiveTradingDays" xlink:href="tlsi-20250331.xsd#tlsi_CommonStockSharePriceMarketPriceNumberOfConsecutiveTradingDays"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_CommonStockSharePriceMarketPriceNumberOfConsecutiveTradingDays" xlink:to="lab_tlsi_CommonStockSharePriceMarketPriceNumberOfConsecutiveTradingDays" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions_1ec9fb26-3965-42bf-a6f9-cbefe20cf336_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecognized compensation expense, RSUs</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Nonvested Award, Excluding Option, Cost Not yet Recognized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions" xlink:to="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PreferredStockConversionShares_e5e2b0f4-8c82-4c40-a060-b794dfbbd278_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockConversionShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock conversion (in shares)</link:label>
    <link:label id="lab_tlsi_PreferredStockConversionShares_label_en-US" xlink:label="lab_tlsi_PreferredStockConversionShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock Conversion, Shares</link:label>
    <link:label id="lab_tlsi_PreferredStockConversionShares_documentation_en-US" xlink:label="lab_tlsi_PreferredStockConversionShares" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Stock Conversion, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PreferredStockConversionShares" xlink:href="tlsi-20250331.xsd#tlsi_PreferredStockConversionShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PreferredStockConversionShares" xlink:to="lab_tlsi_PreferredStockConversionShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_97e4ee2e-e540-4813-bcb8-7d04a0ca68c6_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Undrawn fee, percentage</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Unused Capacity, Commitment Fee Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:to="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodFourMember_6e2a351d-2b6d-40c0-aed4-b6490b7e6c1c_terseLabel_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodFourMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">December 31, 2025</link:label>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodFourMember_label_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodFourMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Feature, Period Four [Member]</link:label>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodFourMember_documentation_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodFourMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Feature, Period Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_RevenueBaseRedemptionFeaturePeriodFourMember" xlink:href="tlsi-20250331.xsd#tlsi_RevenueBaseRedemptionFeaturePeriodFourMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_RevenueBaseRedemptionFeaturePeriodFourMember" xlink:to="lab_tlsi_RevenueBaseRedemptionFeaturePeriodFourMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Asset Acquisition, and Joint Venture Formation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationAndAssetAcquisitionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:to="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Table</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AwardsCloseToMnpiDiscTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpenseAbstract_74c2c686-4952-406b-9c1f-58b049448b19_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income (expense):</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpenseAbstract_label_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Nonoperating Income (Expense) [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncomeExpenseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherNonoperatingIncomeExpenseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNonoperatingIncomeExpenseAbstract" xlink:to="lab_us-gaap_OtherNonoperatingIncomeExpenseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_CommonStockWarrantMember_71cd0bd4-9cde-49ee-9e50-cd5a18b12b74_terseLabel_en-US" xlink:label="lab_tlsi_CommonStockWarrantMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock warrants</link:label>
    <link:label id="lab_tlsi_CommonStockWarrantMember_label_en-US" xlink:label="lab_tlsi_CommonStockWarrantMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock Warrant [Member]</link:label>
    <link:label id="lab_tlsi_CommonStockWarrantMember_documentation_en-US" xlink:label="lab_tlsi_CommonStockWarrantMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock Warrant</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_CommonStockWarrantMember" xlink:href="tlsi-20250331.xsd#tlsi_CommonStockWarrantMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_CommonStockWarrantMember" xlink:to="lab_tlsi_CommonStockWarrantMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_f67217e0-b79e-4ebc-abc3-2490552f408c_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock reserved for future issuance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_label_en-US" xlink:label="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Capital Shares Reserved for Future Issuance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockCapitalSharesReservedForFutureIssuance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:to="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputPriceVolatilityMember_7553d9a0-d0cd-4b5c-95ca-f696c7bf6968_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputPriceVolatilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expected share price volatility</link:label>
    <link:label id="lab_us-gaap_MeasurementInputPriceVolatilityMember_f055fc64-d2eb-41f4-986d-efa33f9ca758_verboseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputPriceVolatilityMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Expected volatility</link:label>
    <link:label id="lab_us-gaap_MeasurementInputPriceVolatilityMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputPriceVolatilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Price Volatility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputPriceVolatilityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MeasurementInputPriceVolatilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputPriceVolatilityMember" xlink:to="lab_us-gaap_MeasurementInputPriceVolatilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year</link:label>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_label_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:to="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_AggtErrCompAmt_label_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompAmt" xlink:to="lab_ecd_AggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_LeaseLiabilityNoncurrent_657928a9-43d2-4ef7-b5de-20caae1c37d6_terseLabel_en-US" xlink:label="lab_tlsi_LeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term lease liabilities</link:label>
    <link:label id="lab_tlsi_LeaseLiabilityNoncurrent_label_en-US" xlink:label="lab_tlsi_LeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease Liability, Noncurrent</link:label>
    <link:label id="lab_tlsi_LeaseLiabilityNoncurrent_documentation_en-US" xlink:label="lab_tlsi_LeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lease Liability, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_LeaseLiabilityNoncurrent" xlink:href="tlsi-20250331.xsd#tlsi_LeaseLiabilityNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_LeaseLiabilityNoncurrent" xlink:to="lab_tlsi_LeaseLiabilityNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_daf10174-58d8-4fbd-b5c2-236ac6a7bd9e_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_LocalPhoneNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LocalPhoneNumber" xlink:to="lab_dei_LocalPhoneNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByLiabilityClassAxis_50eb10aa-d8f6-4715-b4cf-9acbad49ffb3_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liability Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByLiabilityClassAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByLiabilityClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueByLiabilityClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByLiabilityClassAxis" xlink:to="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined</link:label>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_label_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AggtErrCompNotYetDeterminedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:to="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionLineItems_691ca669-5e26-40ab-ad5b-00dea08b6c50_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Line Items]</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionLineItems_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AssetAcquisitionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionLineItems" xlink:to="lab_us-gaap_AssetAcquisitionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_08acc14e-66b2-437d-9528-6f6bdaa4320d_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in operating assets and liabilities:</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Operating Capital [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncreaseDecreaseInOperatingCapitalAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_StockConvertedReverseRecapitalization_21ee00cd-0ddd-4ccd-a2ab-eefe82c57ee0_terseLabel_en-US" xlink:label="lab_tlsi_StockConvertedReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock converted, reverse recapitalization (in shares)</link:label>
    <link:label id="lab_tlsi_StockConvertedReverseRecapitalization_label_en-US" xlink:label="lab_tlsi_StockConvertedReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Converted, Reverse Recapitalization</link:label>
    <link:label id="lab_tlsi_StockConvertedReverseRecapitalization_documentation_en-US" xlink:label="lab_tlsi_StockConvertedReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stock Converted, Reverse Recapitalization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_StockConvertedReverseRecapitalization" xlink:href="tlsi-20250331.xsd#tlsi_StockConvertedReverseRecapitalization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_StockConvertedReverseRecapitalization" xlink:to="lab_tlsi_StockConvertedReverseRecapitalization" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAllowablePercentageOfOutstandingCommonStock_1dcc6b3f-fded-4249-aab1-592e0c3de244_terseLabel_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAllowablePercentageOfOutstandingCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Standby equity purchase agreement, maximum allowable percentage of outstanding common stock</link:label>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAllowablePercentageOfOutstandingCommonStock_label_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAllowablePercentageOfOutstandingCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Standby Equity Purchase Agreement, Maximum Allowable Percentage Of Outstanding Common Stock</link:label>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAllowablePercentageOfOutstandingCommonStock_documentation_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAllowablePercentageOfOutstandingCommonStock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Standby Equity Purchase Agreement, Maximum Allowable Percentage Of Outstanding Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_StandbyEquityPurchaseAgreementMaximumAllowablePercentageOfOutstandingCommonStock" xlink:href="tlsi-20250331.xsd#tlsi_StandbyEquityPurchaseAgreementMaximumAllowablePercentageOfOutstandingCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_StandbyEquityPurchaseAgreementMaximumAllowablePercentageOfOutstandingCommonStock" xlink:to="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAllowablePercentageOfOutstandingCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoTotalCompAmt_label_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PeoTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoTotalCompAmt" xlink:to="lab_ecd_PeoTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent_49222ea9-345d-4c6b-8085-f3aa165d9a4f_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock options exercise price, percentage of fair value</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Purchase Price of Common Stock, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:to="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_a0149262-fed1-4191-8f3c-bb9f788b764b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_SubsequentOrbiMedWarrantsMember_0d2716e4-6caa-42b4-8757-0636ed94f6c6_terseLabel_en-US" xlink:label="lab_tlsi_SubsequentOrbiMedWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent OrbiMed Warrants</link:label>
    <link:label id="lab_tlsi_SubsequentOrbiMedWarrantsMember_label_en-US" xlink:label="lab_tlsi_SubsequentOrbiMedWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent OrbiMed Warrants [Member]</link:label>
    <link:label id="lab_tlsi_SubsequentOrbiMedWarrantsMember_documentation_en-US" xlink:label="lab_tlsi_SubsequentOrbiMedWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Subsequent OrbiMed Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SubsequentOrbiMedWarrantsMember" xlink:href="tlsi-20250331.xsd#tlsi_SubsequentOrbiMedWarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_SubsequentOrbiMedWarrantsMember" xlink:to="lab_tlsi_SubsequentOrbiMedWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_88f4b5a4-cf74-4a36-badd-1790cd0efc10_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Accrued Liabilities</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accrued Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightThresholdNumberOfDaysForWarrantsToBeTransferable_10e18578-f34e-4df8-9afb-225e8f67e3ec_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightThresholdNumberOfDaysForWarrantsToBeTransferable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of warrant or right, threshold number of days for warrants to be transferable</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightThresholdNumberOfDaysForWarrantsToBeTransferable_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightThresholdNumberOfDaysForWarrantsToBeTransferable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Threshold Number of Days for Warrants to be Transferable</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightThresholdNumberOfDaysForWarrantsToBeTransferable_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightThresholdNumberOfDaysForWarrantsToBeTransferable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Threshold Number of Days for Warrants to be Transferable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightThresholdNumberOfDaysForWarrantsToBeTransferable" xlink:href="tlsi-20250331.xsd#tlsi_ClassOfWarrantOrRightThresholdNumberOfDaysForWarrantsToBeTransferable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightThresholdNumberOfDaysForWarrantsToBeTransferable" xlink:to="lab_tlsi_ClassOfWarrantOrRightThresholdNumberOfDaysForWarrantsToBeTransferable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityExTransitionPeriod_18ef8691-d096-4108-91c3-29970cad5b21_terseLabel_en-US" xlink:label="lab_dei_EntityExTransitionPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Ex Transition Period</link:label>
    <link:label id="lab_dei_EntityExTransitionPeriod_label_en-US" xlink:label="lab_dei_EntityExTransitionPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Ex Transition Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityExTransitionPeriod" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityExTransitionPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityExTransitionPeriod" xlink:to="lab_dei_EntityExTransitionPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_08246352-b72f-4ea2-abf7-3240e437c164_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalents, and Restricted Cash</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashAndCashEquivalentsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:to="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_BannockburnFacilityMember_757b13d4-d243-43c9-bed8-5f3608f90322_terseLabel_en-US" xlink:label="lab_tlsi_BannockburnFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Bannockburn Facility</link:label>
    <link:label id="lab_tlsi_BannockburnFacilityMember_label_en-US" xlink:label="lab_tlsi_BannockburnFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Bannockburn Facility [Member]</link:label>
    <link:label id="lab_tlsi_BannockburnFacilityMember_documentation_en-US" xlink:label="lab_tlsi_BannockburnFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Bannockburn Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_BannockburnFacilityMember" xlink:href="tlsi-20250331.xsd#tlsi_BannockburnFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_BannockburnFacilityMember" xlink:to="lab_tlsi_BannockburnFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_95f3a688-cfcd-435b-81c9-344b8e0372c6_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments And Contingencies</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommitmentsAndContingenciesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_GainLossOnChangeInFairValueOfRevenueBaseRedemptionAndWarrantLiability_c336b46c-5eb4-4278-be51-1bca91a03615_negatedTerseLabel_en-US" xlink:label="lab_tlsi_GainLossOnChangeInFairValueOfRevenueBaseRedemptionAndWarrantLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of OrbiMed Warrants and revenue base redemption liabilities</link:label>
    <link:label id="lab_tlsi_GainLossOnChangeInFairValueOfRevenueBaseRedemptionAndWarrantLiability_label_en-US" xlink:label="lab_tlsi_GainLossOnChangeInFairValueOfRevenueBaseRedemptionAndWarrantLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) On Change In Fair Value Of Revenue Base Redemption And Warrant Liability</link:label>
    <link:label id="lab_tlsi_GainLossOnChangeInFairValueOfRevenueBaseRedemptionAndWarrantLiability_documentation_en-US" xlink:label="lab_tlsi_GainLossOnChangeInFairValueOfRevenueBaseRedemptionAndWarrantLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gain (Loss) On Change In Fair Value Of Revenue Base Redemption And Warrant Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_GainLossOnChangeInFairValueOfRevenueBaseRedemptionAndWarrantLiability" xlink:href="tlsi-20250331.xsd#tlsi_GainLossOnChangeInFairValueOfRevenueBaseRedemptionAndWarrantLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_GainLossOnChangeInFairValueOfRevenueBaseRedemptionAndWarrantLiability" xlink:to="lab_tlsi_GainLossOnChangeInFairValueOfRevenueBaseRedemptionAndWarrantLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureAbstract" xlink:to="lab_us-gaap_DebtDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockMember_ee40cf8a-8434-4519-bcce-545c52afb6cc_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common stock, $0.0001 par value</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_68bd7758-39d5-4161-8a04-e1e0e5e71391_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockMember" xlink:to="lab_us-gaap_CommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureAxis_terseLabel_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measure:</link:label>
    <link:label id="lab_ecd_MeasureAxis_label_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureAxis" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_MeasureAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureAxis" xlink:to="lab_ecd_MeasureAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePeriod_31a3c4a7-b988-434c-825c-c4cef74d3895_terseLabel_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation arrangement by share-based payment award, automatic increase period</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePeriod_label_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement By Share-based Payment Award, Automatic Increase Period</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePeriod_documentation_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement By Share-based Payment Award, Automatic Increase Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePeriod" xlink:href="tlsi-20250331.xsd#tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePeriod" xlink:to="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_d828aa46-7a34-4c52-af5c-82a544a5c6c1_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesAuthorized" xlink:to="lab_us-gaap_PreferredStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_6ee06e12-2c9c-4948-873b-f7b7dc137bb7_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Changes in Fair Value of Outstanding Warrant and Tranche Liabilities</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_b0257563-0c6c-4cbf-9e37-7f18c64da6fa_verboseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale of common stock (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_0b35bc20-b953-43c4-86d4-a3c4b82c65d8_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuances (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodFourMember_9913c5e5-22c4-45e9-b374-dd59fb4c7ade_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodFourMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tranche Four</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodFourMember_label_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodFourMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Period Four [Member]</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodFourMember_documentation_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodFourMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Period Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentPeriodFourMember" xlink:href="tlsi-20250331.xsd#tlsi_DerivativeInstrumentPeriodFourMember"/>
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    <link:label id="lab_dei_EntityEmergingGrowthCompany_b8c4186d-18cb-49bb-b934-4cc8f00d81b6_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PublicWarrantsPrivatePlacementWarrantsAndWorkingCapitalWarrantsMember_c4fa393f-028f-47e4-a3c8-ba976d295f6f_terseLabel_en-US" xlink:label="lab_tlsi_PublicWarrantsPrivatePlacementWarrantsAndWorkingCapitalWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Public Warrants, Private Placement Warrants And Working Capital Warrants</link:label>
    <link:label id="lab_tlsi_PublicWarrantsPrivatePlacementWarrantsAndWorkingCapitalWarrantsMember_label_en-US" xlink:label="lab_tlsi_PublicWarrantsPrivatePlacementWarrantsAndWorkingCapitalWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Public Warrants, Private Placement Warrants And Working Capital Warrants [Member]</link:label>
    <link:label id="lab_tlsi_PublicWarrantsPrivatePlacementWarrantsAndWorkingCapitalWarrantsMember_documentation_en-US" xlink:label="lab_tlsi_PublicWarrantsPrivatePlacementWarrantsAndWorkingCapitalWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Public Warrants, Private Placement Warrants And Working Capital Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PublicWarrantsPrivatePlacementWarrantsAndWorkingCapitalWarrantsMember" xlink:href="tlsi-20250331.xsd#tlsi_PublicWarrantsPrivatePlacementWarrantsAndWorkingCapitalWarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PublicWarrantsPrivatePlacementWarrantsAndWorkingCapitalWarrantsMember" xlink:to="lab_tlsi_PublicWarrantsPrivatePlacementWarrantsAndWorkingCapitalWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts_f0cc7ac4-272e-419c-9a92-7ca724d49ffa_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance costs</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustments to Additional Paid in Capital, Stock Issued, Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts" xlink:to="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_acf320fc-8688-448f-915f-7157cadf50e1_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityCentralIndexKey"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCentralIndexKey" xlink:to="lab_dei_EntityCentralIndexKey" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ReverseRecapitalizationDisclosureTextBlock_e77057d0-ee47-4872-a057-c36de164497d_terseLabel_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination</link:label>
    <link:label id="lab_tlsi_ReverseRecapitalizationDisclosureTextBlock_label_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reverse Recapitalization Disclosure [Text Block]</link:label>
    <link:label id="lab_tlsi_ReverseRecapitalizationDisclosureTextBlock_documentation_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reverse Recapitalization Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ReverseRecapitalizationDisclosureTextBlock" xlink:href="tlsi-20250331.xsd#tlsi_ReverseRecapitalizationDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ReverseRecapitalizationDisclosureTextBlock" xlink:to="lab_tlsi_ReverseRecapitalizationDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfInventoryCurrentTableTextBlock_a9b66bad-54d2-4764-b08c-0b3991c573a7_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Components of Inventory</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInventoryCurrentTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Inventory, Current [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfInventoryCurrentTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionTable_c10b561c-55a7-42d7-85e9-6787959c5803_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Table]</link:label>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionTable_label_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeLeaseDescriptionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeLeaseDescriptionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeLeaseDescriptionTable" xlink:to="lab_us-gaap_LesseeLeaseDescriptionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description</link:label>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_label_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_NonGaapMeasureDescriptionTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:to="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_NonPeoNeoAvgCompActuallyPaidAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:to="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities_8fcdb948-96f9-4a49-b003-2a56b6a11b13_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trade payables and accrued liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accounts Payable and Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered [Text Block]</link:label>
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    <link:label id="lab_us-gaap_EquityComponentDomain_0df1dc61-301b-4a05-8ecb-dc0a32a20612_terseLabel_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:label id="lab_us-gaap_EquityComponentDomain_label_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EquityComponentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityComponentDomain" xlink:to="lab_us-gaap_EquityComponentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_1db5e3d9-5540-413c-88b8-87ac8fff5486_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockParOrStatedValuePerShare"/>
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    <link:label id="lab_us-gaap_TemporaryEquitySharesOutstanding_2433fe56-1a68-449f-aa57-ff9fc09b63ef_periodStartLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Convertible preferred stock, beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesOutstanding_00b17504-1164-4583-830e-84850ea8c654_periodEndLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Convertible preferred stock, ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesOutstanding_label_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquitySharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TemporaryEquitySharesOutstanding"/>
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    <link:label id="lab_us-gaap_AccretionExpense_53ef59ec-eddd-4981-b8cf-f2e047e4886d_terseLabel_en-US" xlink:label="lab_us-gaap_AccretionExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accretion of exit fee liability</link:label>
    <link:label id="lab_us-gaap_AccretionExpense_label_en-US" xlink:label="lab_us-gaap_AccretionExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accretion Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccretionExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AccretionExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccretionExpense" xlink:to="lab_us-gaap_AccretionExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_5782a876-d38c-435b-9791-5f1cea2ab290_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock-based compensation</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue"/>
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    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1_8f69ace2-f7a1-41bc-b245-e9658ff6868e_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of contingent earnout liability</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1_f7cee9c5-9fd7-4108-9bf7-e13e694d4c33_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of contingent earnout liability</link:label>
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    <link:label id="lab_us-gaap_MeasurementInputRiskFreeInterestRateMember_56f12d66-04f2-4223-a7e0-982f8efbbfab_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputRiskFreeInterestRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Risk-free interest rate</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputRiskFreeInterestRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MeasurementInputRiskFreeInterestRateMember"/>
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    <link:label id="lab_dei_EntityShellCompany_e9e1a7ff-3773-41ce-8062-0f0c8c85fe89_terseLabel_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:label id="lab_dei_EntityShellCompany_label_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityShellCompany" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityShellCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityShellCompany" xlink:to="lab_dei_EntityShellCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_59aa12b6-3b7e-476c-83f5-47f89e57555b_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityIncorporationStateCountryCode" xlink:to="lab_dei_EntityIncorporationStateCountryCode" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndTitle_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title</link:label>
    <link:label id="lab_ecd_TrdArrIndTitle_label_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Title</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndTitle" xlink:to="lab_ecd_TrdArrIndTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementTable_ddcbf552-b0ad-4790-99eb-133915d3fb69_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementTable" xlink:to="lab_us-gaap_StatementTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseDebt_5ceaec10-4d48-479d-981f-62c34e772d19_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseDebt_label_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InterestExpenseDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseDebt" xlink:to="lab_us-gaap_InterestExpenseDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_SharePriceAsPercentageOfMarketPriceCommencingOnAdvanceNoticeDate_a7d56a9b-cb4f-4fbf-ab9b-ff7ff40ac1b5_terseLabel_en-US" xlink:label="lab_tlsi_SharePriceAsPercentageOfMarketPriceCommencingOnAdvanceNoticeDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchase agreement, sales price, percentage of market price</link:label>
    <link:label id="lab_tlsi_SharePriceAsPercentageOfMarketPriceCommencingOnAdvanceNoticeDate_label_en-US" xlink:label="lab_tlsi_SharePriceAsPercentageOfMarketPriceCommencingOnAdvanceNoticeDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Price As Percentage Of Market Price Commencing On Advance Notice Date</link:label>
    <link:label id="lab_tlsi_SharePriceAsPercentageOfMarketPriceCommencingOnAdvanceNoticeDate_documentation_en-US" xlink:label="lab_tlsi_SharePriceAsPercentageOfMarketPriceCommencingOnAdvanceNoticeDate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share Price As Percentage Of Market Price Commencing On Advance Notice Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SharePriceAsPercentageOfMarketPriceCommencingOnAdvanceNoticeDate" xlink:href="tlsi-20250331.xsd#tlsi_SharePriceAsPercentageOfMarketPriceCommencingOnAdvanceNoticeDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_SharePriceAsPercentageOfMarketPriceCommencingOnAdvanceNoticeDate" xlink:to="lab_tlsi_SharePriceAsPercentageOfMarketPriceCommencingOnAdvanceNoticeDate" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_CounterpartyNameAxis_6da11188-b34a-4b82-ba2b-056df1c04f16_terseLabel_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_srt_CounterpartyNameAxis" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_CounterpartyNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_CounterpartyNameAxis" xlink:to="lab_srt_CounterpartyNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_92cf43ad-6626-43be-9c0f-8a77e32e7195_terseLabel_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Significant Accounting Policies</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SignificantAccountingPoliciesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CityAreaCode_821eeb1b-1730-474c-adb5-3a1e2920c057_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_CityAreaCode"/>
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    <link:label id="lab_us-gaap_LiabilitiesCurrentAbstract_16187d05-4efa-4d17-967a-1e9aa4f39c71_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current liabilities:</link:label>
    <link:label id="lab_us-gaap_LiabilitiesCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Current [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LiabilitiesCurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesCurrentAbstract" xlink:to="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPaidNet_3c96968b-26ae-4bda-9839-8587ca0a2ec1_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest paid</link:label>
    <link:label id="lab_us-gaap_InterestPaidNet_label_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Paid, Excluding Capitalized Interest, Operating Activities</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPaidNet" xlink:to="lab_us-gaap_InterestPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted [Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:to="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_363f8edb-794a-420d-8463-13b0cc2fe430_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 1</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</link:label>
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    <link:label id="lab_tlsi_ClassOfWarrantOrRightNumberOfOperatingEntitiesHoldingWarrants_4b40c9e6-e429-4cb0-9ba9-6f7cd51581a5_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightNumberOfOperatingEntitiesHoldingWarrants" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Number Of Operating Entities Holding Warrants</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightNumberOfOperatingEntitiesHoldingWarrants_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightNumberOfOperatingEntitiesHoldingWarrants" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Number Of Operating Entities Holding Warrants</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightNumberOfOperatingEntitiesHoldingWarrants_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightNumberOfOperatingEntitiesHoldingWarrants" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Number Of Operating Entities Holding Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightNumberOfOperatingEntitiesHoldingWarrants" xlink:href="tlsi-20250331.xsd#tlsi_ClassOfWarrantOrRightNumberOfOperatingEntitiesHoldingWarrants"/>
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    <link:label id="lab_us-gaap_AssetsCurrent_56e5aafd-874b-41f2-acea-37aee8504523_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total current assets</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AssetsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsCurrent" xlink:to="lab_us-gaap_AssetsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:to="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RestatementDomain_1c3ccb8b-ba76-46bf-b4b4-5959b01b092a_terseLabel_en-US" xlink:label="lab_srt_RestatementDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revision of Prior Period [Domain]</link:label>
    <link:label id="lab_srt_RestatementDomain_label_en-US" xlink:label="lab_srt_RestatementDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revision of Prior Period [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RestatementDomain" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_RestatementDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RestatementDomain" xlink:to="lab_srt_RestatementDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockMember_716b693f-60c2-4779-a3aa-194d28c78832_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock</link:label>
    <link:label id="lab_us-gaap_PreferredStockMember_label_en-US" xlink:label="lab_us-gaap_PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockMember" xlink:to="lab_us-gaap_PreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_WarrantsIssuedInConnectionWithDebtValue_ff9bff57-cedc-4547-8446-10c3eaed57de_negatedTerseLabel_en-US" xlink:label="lab_tlsi_WarrantsIssuedInConnectionWithDebtValue" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Fair value of warrants issued related to OrbiMed debt</link:label>
    <link:label id="lab_tlsi_WarrantsIssuedInConnectionWithDebtValue_label_en-US" xlink:label="lab_tlsi_WarrantsIssuedInConnectionWithDebtValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrants Issued In Connection With Debt, Value</link:label>
    <link:label id="lab_tlsi_WarrantsIssuedInConnectionWithDebtValue_documentation_en-US" xlink:label="lab_tlsi_WarrantsIssuedInConnectionWithDebtValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Warrants Issued In Connection With Debt, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_WarrantsIssuedInConnectionWithDebtValue" xlink:href="tlsi-20250331.xsd#tlsi_WarrantsIssuedInConnectionWithDebtValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_WarrantsIssuedInConnectionWithDebtValue" xlink:to="lab_tlsi_WarrantsIssuedInConnectionWithDebtValue" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodOneMember_859de3ed-d22e-4d90-b31a-48c256285df0_terseLabel_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">March 31, 2025</link:label>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodOneMember_label_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodOneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Feature, Period One [Member]</link:label>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodOneMember_documentation_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodOneMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Feature, Period One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_RevenueBaseRedemptionFeaturePeriodOneMember" xlink:href="tlsi-20250331.xsd#tlsi_RevenueBaseRedemptionFeaturePeriodOneMember"/>
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    <link:label id="lab_us-gaap_DebtInstrumentTable_a5cf1607-a9b8-430d-8330-69c4d2d904f6_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTable_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTable" xlink:to="lab_us-gaap_DebtInstrumentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PrepaymentPremiumRatePeriodTwoMember_f182a3e6-0001-4bc1-9714-476023213b0b_terseLabel_en-US" xlink:label="lab_tlsi_PrepaymentPremiumRatePeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">12 to 24 Months</link:label>
    <link:label id="lab_tlsi_PrepaymentPremiumRatePeriodTwoMember_label_en-US" xlink:label="lab_tlsi_PrepaymentPremiumRatePeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepayment Premium Rate, Period Two [Member]</link:label>
    <link:label id="lab_tlsi_PrepaymentPremiumRatePeriodTwoMember_documentation_en-US" xlink:label="lab_tlsi_PrepaymentPremiumRatePeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Prepayment Premium Rate, Period Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PrepaymentPremiumRatePeriodTwoMember" xlink:href="tlsi-20250331.xsd#tlsi_PrepaymentPremiumRatePeriodTwoMember"/>
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    <link:label id="lab_us-gaap_LongTermDebtNoncurrent_d80afe5d-f81a-4572-91b1-3f4667f8952d_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term debt, net of unamortized discount and debt issuance costs</link:label>
    <link:label id="lab_us-gaap_LongTermDebtNoncurrent_label_en-US" xlink:label="lab_us-gaap_LongTermDebtNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Excluding Current Maturities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LongTermDebtNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtNoncurrent" xlink:to="lab_us-gaap_LongTermDebtNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock_85e5afa7-6ff9-4368-80fb-030817cf22d9_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_35b38047-5d40-4a09-9466-6a6a78f99666_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Options, weighted average fair value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue"/>
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    <link:label id="lab_us-gaap_MeasurementInputExpectedTermMember_6e76d095-8c58-4ee2-88bb-902047aadf52_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputExpectedTermMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expected term (years)</link:label>
    <link:label id="lab_us-gaap_MeasurementInputExpectedTermMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputExpectedTermMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Expected Term [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputExpectedTermMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MeasurementInputExpectedTermMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputExpectedTermMember" xlink:to="lab_us-gaap_MeasurementInputExpectedTermMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_9efc94d2-3e9b-4311-8535-f7f957fd3d5b_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsequentEventTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeAxis" xlink:to="lab_us-gaap_SubsequentEventTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_94a861b7-c994-45c3-a209-bd0c9386e6c0_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeTaxDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:to="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_f5c007d7-000a-4c15-b654-454f614bcb71_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EarningsPerShareAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareAbstract" xlink:to="lab_us-gaap_EarningsPerShareAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityAbstract_52b3d2d6-f398-4e37-b960-d058b8827f79_terseLabel_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stockholders&#8217; deficit:</link:label>
    <link:label id="lab_us-gaap_EquityAbstract_label_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityAbstract" xlink:to="lab_us-gaap_EquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DebtInstrumentPaidInKindInterestTerm_c46ec5c9-0708-45c1-92dc-2d98c84f090e_terseLabel_en-US" xlink:label="lab_tlsi_DebtInstrumentPaidInKindInterestTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Paid in kind interest, term</link:label>
    <link:label id="lab_tlsi_DebtInstrumentPaidInKindInterestTerm_label_en-US" xlink:label="lab_tlsi_DebtInstrumentPaidInKindInterestTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Paid-In-Kind Interest, Term</link:label>
    <link:label id="lab_tlsi_DebtInstrumentPaidInKindInterestTerm_documentation_en-US" xlink:label="lab_tlsi_DebtInstrumentPaidInKindInterestTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Paid-In-Kind Interest, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DebtInstrumentPaidInKindInterestTerm" xlink:href="tlsi-20250331.xsd#tlsi_DebtInstrumentPaidInKindInterestTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DebtInstrumentPaidInKindInterestTerm" xlink:to="lab_tlsi_DebtInstrumentPaidInKindInterestTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_66706a02-9f00-4720-99e4-a7e0030e78b6_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated deficit</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_53043b2a-1be8-45ad-8236-c9bf0488ba69_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accumulated deficit</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockDomain_4feaa871-b538-4f89-ae86-ec7fd083222d_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfStockDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockDomain" xlink:to="lab_us-gaap_ClassOfStockDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInInventories_6943a650-8b99-4f5a-a5b9-92ef262d2eda_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInInventories" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Inventory, net</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInInventories" xlink:to="lab_us-gaap_IncreaseDecreaseInInventories" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplementalCashFlowElementsAbstract_c18ee7fb-90f2-4762-82b4-81c7ea8d414c_terseLabel_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowElementsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental disclosures of cash flow information:</link:label>
    <link:label id="lab_us-gaap_SupplementalCashFlowElementsAbstract_label_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowElementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supplemental Cash Flow Elements [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalCashFlowElementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SupplementalCashFlowElementsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SupplementalCashFlowElementsAbstract" xlink:to="lab_us-gaap_SupplementalCashFlowElementsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_03972fbe-a05f-4c0c-9190-56e350bff321_terseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General and administrative</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:to="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightSharesIssuedDuringPeriod_841b36f4-7f4f-4426-a98f-1ce27da3b7c6_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightSharesIssuedDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuances (in shares)</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightSharesIssuedDuringPeriod_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightSharesIssuedDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Shares Issued During Period</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightSharesIssuedDuringPeriod_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightSharesIssuedDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Shares Issued During Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightSharesIssuedDuringPeriod" xlink:href="tlsi-20250331.xsd#tlsi_ClassOfWarrantOrRightSharesIssuedDuringPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightSharesIssuedDuringPeriod" xlink:to="lab_tlsi_ClassOfWarrantOrRightSharesIssuedDuringPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_terseLabel_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Available</link:label>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_label_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Securities Aggregate Available Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_TrdArrSecuritiesAggAvailAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:to="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_EqtyAwrdsAdjsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsMember" xlink:to="lab_ecd_EqtyAwrdsAdjsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFeeAmount_5a9bcc5d-63fc-4c0d-9fd2-9e29c741e116_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFeeAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Administrative fee</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFeeAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFeeAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Fee Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFeeAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentFeeAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFeeAmount" xlink:to="lab_us-gaap_DebtInstrumentFeeAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_2ba3001c-8c82-4a47-840f-7c9cc9c5d0b5_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by financing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Cash Provided by (Used in) Financing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_terseLabel_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Securities</link:label>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_label_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Underlying Securities Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AwardUndrlygSecuritiesAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:to="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerecognitionOfFinanceLeaseRightOfUseAsset_7c61c184-fe8f-44a6-a2dd-b8b25a64dd5c_negatedTerseLabel_en-US" xlink:label="lab_tlsi_DerecognitionOfFinanceLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Derecognition of finance lease right-of-use asset</link:label>
    <link:label id="lab_tlsi_DerecognitionOfFinanceLeaseRightOfUseAsset_label_en-US" xlink:label="lab_tlsi_DerecognitionOfFinanceLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derecognition Of Finance Lease Right-Of-Use Asset</link:label>
    <link:label id="lab_tlsi_DerecognitionOfFinanceLeaseRightOfUseAsset_documentation_en-US" xlink:label="lab_tlsi_DerecognitionOfFinanceLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derecognition Of Finance Lease Right-Of-Use Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerecognitionOfFinanceLeaseRightOfUseAsset" xlink:href="tlsi-20250331.xsd#tlsi_DerecognitionOfFinanceLeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DerecognitionOfFinanceLeaseRightOfUseAsset" xlink:to="lab_tlsi_DerecognitionOfFinanceLeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PrepaymentPremiumRatePeriodOneMember_102b4cbc-48c0-4919-917a-2a66ada67551_terseLabel_en-US" xlink:label="lab_tlsi_PrepaymentPremiumRatePeriodOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Within 12 Months</link:label>
    <link:label id="lab_tlsi_PrepaymentPremiumRatePeriodOneMember_label_en-US" xlink:label="lab_tlsi_PrepaymentPremiumRatePeriodOneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepayment Premium Rate, Period One [Member]</link:label>
    <link:label id="lab_tlsi_PrepaymentPremiumRatePeriodOneMember_documentation_en-US" xlink:label="lab_tlsi_PrepaymentPremiumRatePeriodOneMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Prepayment Premium Rate, Period One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PrepaymentPremiumRatePeriodOneMember" xlink:href="tlsi-20250331.xsd#tlsi_PrepaymentPremiumRatePeriodOneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PrepaymentPremiumRatePeriodOneMember" xlink:to="lab_tlsi_PrepaymentPremiumRatePeriodOneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AmendmentFlag_706314b6-bf79-490c-9939-378f74d63948_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:label id="lab_dei_AmendmentFlag_label_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_AmendmentFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AmendmentFlag" xlink:to="lab_dei_AmendmentFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DebtInstrumentActivityRollForward_dc539a2d-5f76-441f-8ea3-9b6447cfa363_terseLabel_en-US" xlink:label="lab_tlsi_DebtInstrumentActivityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Activity [Roll Forward]</link:label>
    <link:label id="lab_tlsi_DebtInstrumentActivityRollForward_label_en-US" xlink:label="lab_tlsi_DebtInstrumentActivityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Activity [Roll Forward]</link:label>
    <link:label id="lab_tlsi_DebtInstrumentActivityRollForward_documentation_en-US" xlink:label="lab_tlsi_DebtInstrumentActivityRollForward" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DebtInstrumentActivityRollForward" xlink:href="tlsi-20250331.xsd#tlsi_DebtInstrumentActivityRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DebtInstrumentActivityRollForward" xlink:to="lab_tlsi_DebtInstrumentActivityRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_e243cab1-bcd4-4a82-b128-edbd7ac92a1b_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnSaleOfPropertyPlantEquipment_dc2dc48a-6b14-46fc-b84d-3fe63fc50dad_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Loss on disposal of property and equipment</link:label>
    <link:label id="lab_us-gaap_GainLossOnSaleOfPropertyPlantEquipment_label_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Disposition of Property Plant Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GainLossOnSaleOfPropertyPlantEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:to="lab_us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote</link:label>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AdjToNonPeoNeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:to="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_terseLabel_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs)</link:label>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_label_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockAppreciationRightsSARSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:to="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DebtInstrumentPrepaymentPremiumRate_8d28a0ce-c823-48d2-ade5-358b986de682_terseLabel_en-US" xlink:label="lab_tlsi_DebtInstrumentPrepaymentPremiumRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, prepayment premium rate</link:label>
    <link:label id="lab_tlsi_DebtInstrumentPrepaymentPremiumRate_label_en-US" xlink:label="lab_tlsi_DebtInstrumentPrepaymentPremiumRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Prepayment Premium Rate</link:label>
    <link:label id="lab_tlsi_DebtInstrumentPrepaymentPremiumRate_documentation_en-US" xlink:label="lab_tlsi_DebtInstrumentPrepaymentPremiumRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Prepayment Premium Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DebtInstrumentPrepaymentPremiumRate" xlink:href="tlsi-20250331.xsd#tlsi_DebtInstrumentPrepaymentPremiumRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DebtInstrumentPrepaymentPremiumRate" xlink:to="lab_tlsi_DebtInstrumentPrepaymentPremiumRate" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriod_8e77ca67-b8d8-47f2-85ba-2b84c331464b_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative instrument, contingent consideration, liability, earnout period</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriod_label_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Contingent Consideration, Liability, Earnout Period</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriod_documentation_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Contingent Consideration, Liability, Earnout Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriod" xlink:href="tlsi-20250331.xsd#tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriod" xlink:to="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward_9dcd653c-d6d8-4035-ac5c-7828c3c00ea8_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Temporary Equity [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Temporary Equity [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncreaseDecreaseInTemporaryEquityRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:to="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GrossProfit_0c3434c2-0a0a-4975-b1fd-540c394c1a10_totalLabel_en-US" xlink:label="lab_us-gaap_GrossProfit" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Gross profit</link:label>
    <link:label id="lab_us-gaap_GrossProfit_label_en-US" xlink:label="lab_us-gaap_GrossProfit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gross Profit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GrossProfit" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_GrossProfit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GrossProfit" xlink:to="lab_us-gaap_GrossProfit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock_8b92b40e-c4d9-471e-85e3-fc17cfec61b7_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Restricted Cash</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restrictions on Cash and Cash Equivalents [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PrepaymentPremiumRatePeriodFiveMember_d33c2e54-5a98-4c40-86f2-598b0ede7c29_terseLabel_en-US" xlink:label="lab_tlsi_PrepaymentPremiumRatePeriodFiveMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">After 48 Months</link:label>
    <link:label id="lab_tlsi_PrepaymentPremiumRatePeriodFiveMember_label_en-US" xlink:label="lab_tlsi_PrepaymentPremiumRatePeriodFiveMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepayment Premium Rate, Period Five [Member]</link:label>
    <link:label id="lab_tlsi_PrepaymentPremiumRatePeriodFiveMember_documentation_en-US" xlink:label="lab_tlsi_PrepaymentPremiumRatePeriodFiveMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Prepayment Premium Rate, Period Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PrepaymentPremiumRatePeriodFiveMember" xlink:href="tlsi-20250331.xsd#tlsi_PrepaymentPremiumRatePeriodFiveMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PrepaymentPremiumRatePeriodFiveMember" xlink:to="lab_tlsi_PrepaymentPremiumRatePeriodFiveMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardGrantDateFairValue_terseLabel_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value as of Grant Date</link:label>
    <link:label id="lab_ecd_AwardGrantDateFairValue_label_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardGrantDateFairValue" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AwardGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardGrantDateFairValue" xlink:to="lab_ecd_AwardGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionStockPriceThreshold_87941e20-eca2-4d3b-af70-42a19a709696_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionStockPriceThreshold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrant redemption condition, share price (in dollars per share)</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionStockPriceThreshold_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionStockPriceThreshold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Conversion Stock Price Threshold</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionStockPriceThreshold_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionStockPriceThreshold" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Conversion Stock Price Threshold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightConversionStockPriceThreshold" xlink:href="tlsi-20250331.xsd#tlsi_ClassOfWarrantOrRightConversionStockPriceThreshold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightConversionStockPriceThreshold" xlink:to="lab_tlsi_ClassOfWarrantOrRightConversionStockPriceThreshold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_9c3456d7-e8f0-47b6-a01d-192d9e5d7c90_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 2</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel2Member" xlink:to="lab_us-gaap_FairValueInputsLevel2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_fa4ba997-38fa-45a2-bc0d-fbe0acb92b8f_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of stock (in shares)</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_label_en-US" xlink:label="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Number of Shares Issued in Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:to="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_2e690aa4-d825-464e-9d8a-a6c252d5e9cf_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureTextBlock" xlink:to="lab_us-gaap_DebtDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_90797513-df16-42d2-9a24-412070984975_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ContingentConsiderationLiabilityShares_5714020c-1faf-4d5b-895b-44c6618ecec5_terseLabel_en-US" xlink:label="lab_tlsi_ContingentConsiderationLiabilityShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares unvested (in shares)</link:label>
    <link:label id="lab_tlsi_ContingentConsiderationLiabilityShares_label_en-US" xlink:label="lab_tlsi_ContingentConsiderationLiabilityShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contingent Consideration, Liability, Shares</link:label>
    <link:label id="lab_tlsi_ContingentConsiderationLiabilityShares_documentation_en-US" xlink:label="lab_tlsi_ContingentConsiderationLiabilityShares" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Shares Unvested</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ContingentConsiderationLiabilityShares" xlink:href="tlsi-20250331.xsd#tlsi_ContingentConsiderationLiabilityShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ContingentConsiderationLiabilityShares" xlink:to="lab_tlsi_ContingentConsiderationLiabilityShares" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RecoveryOfErrCompDisclosureLineItems_label_en-US" xlink:label="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Erroneously Awarded Compensation Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_RecoveryOfErrCompDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:to="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_b1655cb0-ec5f-4d0f-bc96-c36ddd917bc7_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale of common stock</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_de7d18bb-bcb5-4d06-a6f0-f951e70c9e65_verboseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Issuance of stock</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesNoncurrent_a489a046-4be9-4abf-8a5e-28dcd95b7d36_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrant and SEPA liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesNoncurrent_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilitiesNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativeLiabilitiesNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilitiesNoncurrent" xlink:to="lab_us-gaap_DerivativeLiabilitiesNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressPostalZipCode_d2efa80c-b339-47a6-afc2-0207bcf7df8d_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityAddressPostalZipCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressPostalZipCode" xlink:to="lab_dei_EntityAddressPostalZipCode" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdvertisingExpense_0394322e-69cc-465a-87b2-09f08c5a22f7_terseLabel_en-US" xlink:label="lab_us-gaap_AdvertisingExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Advertising expense</link:label>
    <link:label id="lab_us-gaap_AdvertisingExpense_label_en-US" xlink:label="lab_us-gaap_AdvertisingExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Advertising Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdvertisingExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AdvertisingExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdvertisingExpense" xlink:to="lab_us-gaap_AdvertisingExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightOwnershipLimitation_1e57edd6-8b67-4862-a427-926fe638f71e_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightOwnershipLimitation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchase agreement, ownership limitation</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightOwnershipLimitation_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightOwnershipLimitation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Ownership Limitation</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightOwnershipLimitation_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightOwnershipLimitation" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Ownership Limitation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightOwnershipLimitation" xlink:href="tlsi-20250331.xsd#tlsi_ClassOfWarrantOrRightOwnershipLimitation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightOwnershipLimitation" xlink:to="lab_tlsi_ClassOfWarrantOrRightOwnershipLimitation" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDateAxis_terseLabel_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date:</link:label>
    <link:label id="lab_ecd_RestatementDateAxis_label_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDateAxis" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_RestatementDateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDateAxis" xlink:to="lab_ecd_RestatementDateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_Security12bTitle_1f307c4f-509b-4fd6-873e-09892de38f82_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:label id="lab_dei_Security12bTitle_label_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_Security12bTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_Security12bTitle" xlink:to="lab_dei_Security12bTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockValue_9555e673-d876-4634-ab22-a29a3508a531_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, $0.0001 par value per share. Authorized 400,000,000 shares at March&#160;31, 2025 and December&#160;31, 2024, respectively; issued and outstanding, 32,272,462 and 31,279,264 shares at March&#160;31, 2025, and December&#160;31, 2024, respectively.</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockValue" xlink:to="lab_us-gaap_CommonStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_A2009PlanMember_a2ef2699-adf5-4fde-ae10-4eb39dbb3bd1_terseLabel_en-US" xlink:label="lab_tlsi_A2009PlanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2009 Plan</link:label>
    <link:label id="lab_tlsi_A2009PlanMember_label_en-US" xlink:label="lab_tlsi_A2009PlanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2009 Plan [Member]</link:label>
    <link:label id="lab_tlsi_A2009PlanMember_documentation_en-US" xlink:label="lab_tlsi_A2009PlanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2009 Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_A2009PlanMember" xlink:href="tlsi-20250331.xsd#tlsi_A2009PlanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_A2009PlanMember" xlink:to="lab_tlsi_A2009PlanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodAxis_897c1db9-ebd7-4347-8ede-468f687a0f64_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Period [Axis]</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodAxis_label_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Period [Axis]</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodAxis_documentation_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentPeriodAxis" xlink:href="tlsi-20250331.xsd#tlsi_DerivativeInstrumentPeriodAxis"/>
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    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:to="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_f36dfe3d-c9b2-4cfd-af62-a9ea9c9cdabe_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, at Carrying Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodThreeMember_ebd2ab6c-7a41-4001-b179-9574c078f93e_terseLabel_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodThreeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">September 30, 2025</link:label>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodThreeMember_label_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodThreeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Feature, Period Three [Member]</link:label>
    <link:label id="lab_tlsi_RevenueBaseRedemptionFeaturePeriodThreeMember_documentation_en-US" xlink:label="lab_tlsi_RevenueBaseRedemptionFeaturePeriodThreeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Revenue Base Redemption Feature, Period Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_RevenueBaseRedemptionFeaturePeriodThreeMember" xlink:href="tlsi-20250331.xsd#tlsi_RevenueBaseRedemptionFeaturePeriodThreeMember"/>
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    <link:label id="lab_tlsi_RestrictedStockUnitsAndPerformanceSharesMember_7bca1154-2bf4-4236-ae95-f569a88fabd8_terseLabel_en-US" xlink:label="lab_tlsi_RestrictedStockUnitsAndPerformanceSharesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted And Performance Stock Units</link:label>
    <link:label id="lab_tlsi_RestrictedStockUnitsAndPerformanceSharesMember_label_en-US" xlink:label="lab_tlsi_RestrictedStockUnitsAndPerformanceSharesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock Units And Performance Shares [Member]</link:label>
    <link:label id="lab_tlsi_RestrictedStockUnitsAndPerformanceSharesMember_documentation_en-US" xlink:label="lab_tlsi_RestrictedStockUnitsAndPerformanceSharesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restricted Stock Units And Performance Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_RestrictedStockUnitsAndPerformanceSharesMember" xlink:href="tlsi-20250331.xsd#tlsi_RestrictedStockUnitsAndPerformanceSharesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_RestrictedStockUnitsAndPerformanceSharesMember" xlink:to="lab_tlsi_RestrictedStockUnitsAndPerformanceSharesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss_bfe2ee9d-bc38-49cd-8ab9-5cb198beb77b_negatedLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Change in Unrealized (Gains) Losses</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss_97a4b3c3-48a8-4e89-b072-74266a8ec047_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in unrealized gain</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Liability, Recurring Basis, Still Held, Unrealized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_label_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember"/>
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    <link:label id="lab_tlsi_PublicWarrantsMember_0d82978e-443d-478e-a4aa-efe26b4fd64b_terseLabel_en-US" xlink:label="lab_tlsi_PublicWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Public Warrants</link:label>
    <link:label id="lab_tlsi_PublicWarrantsMember_label_en-US" xlink:label="lab_tlsi_PublicWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Public Warrants [Member]</link:label>
    <link:label id="lab_tlsi_PublicWarrantsMember_documentation_en-US" xlink:label="lab_tlsi_PublicWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Public Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PublicWarrantsMember" xlink:href="tlsi-20250331.xsd#tlsi_PublicWarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PublicWarrantsMember" xlink:to="lab_tlsi_PublicWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryRawMaterials_7bc351d3-9592-43d1-a6b8-067905ae2e56_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryRawMaterials" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Raw materials</link:label>
    <link:label id="lab_us-gaap_InventoryRawMaterials_label_en-US" xlink:label="lab_us-gaap_InventoryRawMaterials" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory, Raw Materials, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryRawMaterials" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InventoryRawMaterials"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryRawMaterials" xlink:to="lab_us-gaap_InventoryRawMaterials" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_SaleOfStockAuthorizedAmountValue_97c4dbe3-d5d1-44c6-a27e-dd71692ae206_terseLabel_en-US" xlink:label="lab_tlsi_SaleOfStockAuthorizedAmountValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of stock, authorized amount</link:label>
    <link:label id="lab_tlsi_SaleOfStockAuthorizedAmountValue_label_en-US" xlink:label="lab_tlsi_SaleOfStockAuthorizedAmountValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale Of Stock, Authorized Amount, Value</link:label>
    <link:label id="lab_tlsi_SaleOfStockAuthorizedAmountValue_documentation_en-US" xlink:label="lab_tlsi_SaleOfStockAuthorizedAmountValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sale Of Stock, Authorized Amount, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SaleOfStockAuthorizedAmountValue" xlink:href="tlsi-20250331.xsd#tlsi_SaleOfStockAuthorizedAmountValue"/>
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    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresLineItems_117384db-8274-40ad-918a-b6ef2ab677b6_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosures [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresLineItems" xlink:to="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain_00ebdc7e-57e5-480a-93d2-85b54a1f5c75_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value by Liability Class [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value by Liability Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_terseLabel_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_label_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember"/>
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    <link:label id="lab_us-gaap_PreferredStockValue_431c335c-bb12-48a7-adb5-a5c6052388ed_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Stock, Convertible Series A, $0.0001 par value per share, $10.00 liquidation value per share. Authorized 10,000,000 shares at March&#160;31, 2025 and December&#160;31, 2024, respectively; issued and outstanding, 3,620,002 and 3,985,002 shares at March&#160;31, 2025, and December&#160;31, 2024, respectively.</link:label>
    <link:label id="lab_us-gaap_PreferredStockValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PreferredStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockValue" xlink:to="lab_us-gaap_PreferredStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryFinishedGoods_15f8791c-e572-43d2-aeaf-69c276a31d77_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryFinishedGoods" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finished goods</link:label>
    <link:label id="lab_us-gaap_InventoryFinishedGoods_label_en-US" xlink:label="lab_us-gaap_InventoryFinishedGoods" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory, Finished Goods, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryFinishedGoods" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InventoryFinishedGoods"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryFinishedGoods" xlink:to="lab_us-gaap_InventoryFinishedGoods" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife_1fa18964-f00c-4de3-be0d-f1d9ab5673b3_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, plant and equipment, useful life</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Useful Life</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PropertyPlantAndEquipmentUsefulLife"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockMember_1e91a814-0123-4041-b544-3e2d8beaebdd_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock</link:label>
    <link:label id="lab_us-gaap_EmployeeStockMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Employee Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EmployeeStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockMember" xlink:to="lab_us-gaap_EmployeeStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionAndRetirementsOfConvertibleSecurities_c484d6be-4933-4fb8-98ef-40b30d697b9e_negatedTerseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionAndRetirementsOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Retirements/Conversions (in shares)</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionAndRetirementsOfConvertibleSecurities_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionAndRetirementsOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant Or Right, Conversion And Retirements Of Convertible Securities</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionAndRetirementsOfConvertibleSecurities_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionAndRetirementsOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class of Warrant Or Right, Conversion And Retirements Of Convertible Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightConversionAndRetirementsOfConvertibleSecurities" xlink:href="tlsi-20250331.xsd#tlsi_ClassOfWarrantOrRightConversionAndRetirementsOfConvertibleSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightConversionAndRetirementsOfConvertibleSecurities" xlink:to="lab_tlsi_ClassOfWarrantOrRightConversionAndRetirementsOfConvertibleSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DepreciationAndAmortization_b866fddd-b32e-4780-8efb-1fd18747325d_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation</link:label>
    <link:label id="lab_us-gaap_DepreciationAndAmortization_190d0624-5e99-4e35-9c9d-0dab868d8cdf_verboseLabel_en-US" xlink:label="lab_us-gaap_DepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization</link:label>
    <link:label id="lab_us-gaap_DepreciationAndAmortization_label_en-US" xlink:label="lab_us-gaap_DepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation, Depletion and Amortization, Nonproduction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DepreciationAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DepreciationAndAmortization" xlink:to="lab_us-gaap_DepreciationAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_86f84dc9-08ed-4b70-8a41-b57939e8fa24_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net loss per common share, basic (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EarningsPerShareBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasic" xlink:to="lab_us-gaap_EarningsPerShareBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_ae36c548-4b07-407a-9d7e-1eaa7b4c7726_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from the issuance of common stock</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ProceedsFromIssuanceOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_SubsequentOrbiMedWarrantsEntityOneMember_287e1eee-8400-44c1-9d02-73eaf88b9df2_terseLabel_en-US" xlink:label="lab_tlsi_SubsequentOrbiMedWarrantsEntityOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent OrbiMed Warrants, Entity One</link:label>
    <link:label id="lab_tlsi_SubsequentOrbiMedWarrantsEntityOneMember_label_en-US" xlink:label="lab_tlsi_SubsequentOrbiMedWarrantsEntityOneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent OrbiMed Warrants, Entity One [Member]</link:label>
    <link:label id="lab_tlsi_SubsequentOrbiMedWarrantsEntityOneMember_documentation_en-US" xlink:label="lab_tlsi_SubsequentOrbiMedWarrantsEntityOneMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Subsequent OrbiMed Warrants, Entity One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SubsequentOrbiMedWarrantsEntityOneMember" xlink:href="tlsi-20250331.xsd#tlsi_SubsequentOrbiMedWarrantsEntityOneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_SubsequentOrbiMedWarrantsEntityOneMember" xlink:to="lab_tlsi_SubsequentOrbiMedWarrantsEntityOneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote</link:label>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToPeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AdjToPeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToPeoCompFnTextBlock" xlink:to="lab_ecd_AdjToPeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AwardTmgMnpiDiscTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:to="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_649bf801-973e-4ff3-958e-081c1fbdc1aa_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation arrangement by share-based payment award, expiration period</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Expiration Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:to="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization_7b187ca1-179d-417d-9a1a-72205cb7ad4e_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property and equipment, net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment and Finance Lease Right-of-Use Asset, after Accumulated Depreciation and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeasePrincipalPayments_255a6727-3621-4c9f-b857-cc74df5be57d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payments on finance lease liabilities</link:label>
    <link:label id="lab_us-gaap_FinanceLeasePrincipalPayments_label_en-US" xlink:label="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Principal Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeasePrincipalPayments" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FinanceLeasePrincipalPayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeasePrincipalPayments" xlink:to="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_LoanFacilityMember_44dc1e63-b300-48fd-ae1f-d3d180c996d6_terseLabel_en-US" xlink:label="lab_tlsi_LoanFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan Facility</link:label>
    <link:label id="lab_tlsi_LoanFacilityMember_label_en-US" xlink:label="lab_tlsi_LoanFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan Facility [Member]</link:label>
    <link:label id="lab_tlsi_LoanFacilityMember_documentation_en-US" xlink:label="lab_tlsi_LoanFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_LoanFacilityMember" xlink:href="tlsi-20250331.xsd#tlsi_LoanFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_LoanFacilityMember" xlink:to="lab_tlsi_LoanFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid_f1719783-45ad-425c-a658-9b1c4a5a7efe_terseLabel_en-US" xlink:label="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed asset purchases included in trade payables and accrued expenses</link:label>
    <link:label id="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid_label_en-US" xlink:label="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital Expenditures Incurred but Not yet Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CapitalExpendituresIncurredButNotYetPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:to="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AggtPnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:to="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_32be3b66-27ed-4cfb-abab-232b25450b96_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net loss attributable to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_7e80304d-3680-453e-b4ad-62a68a468e61_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net loss attributable to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_2e2a4b5e-1d47-4794-ad1d-0504c9ac5bde_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property and Equipment</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PropertyPlantAndEquipmentPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_CompActuallyPaidVsOtherMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_392c7c8e-8ba6-40bc-b936-56c26e74a1af_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total current liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Current</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesCurrent" xlink:to="lab_us-gaap_LiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember"/>
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    <link:label id="lab_tlsi_DerivativeInstrumentPeriodOneMember_865e957b-17e7-4e14-899f-c73f9bff538e_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tranche One</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodOneMember_label_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodOneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Period One [Member]</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodOneMember_documentation_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodOneMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Period One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentPeriodOneMember" xlink:href="tlsi-20250331.xsd#tlsi_DerivativeInstrumentPeriodOneMember"/>
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    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions_1be0d102-0b03-41c7-8ca4-8f1051d849a5_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecognized compensation expense, options</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Nonvested Award, Option, Cost Not yet Recognized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:to="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScenarioPreviouslyReportedMember_3d3d194a-e85e-425a-8c3c-ccbd64c039c6_terseLabel_en-US" xlink:label="lab_srt_ScenarioPreviouslyReportedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Previously Reported</link:label>
    <link:label id="lab_srt_ScenarioPreviouslyReportedMember_label_en-US" xlink:label="lab_srt_ScenarioPreviouslyReportedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Previously Reported [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScenarioPreviouslyReportedMember" xlink:href="https://xbrl.fasb.org/srt/2024/elts/srt-2024.xsd#srt_ScenarioPreviouslyReportedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScenarioPreviouslyReportedMember" xlink:to="lab_srt_ScenarioPreviouslyReportedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_a25fbb01-877b-40a5-9fa1-2a3b7f5a1799_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskCreditRisk_65743ff3-9ad6-4eb2-9027-9d0a0dfad2d8_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskCreditRisk" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentrations of Credit Risk and Other Risks and Uncertainties</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskCreditRisk_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskCreditRisk" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk, Credit Risk, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskCreditRisk" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ConcentrationRiskCreditRisk"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskCreditRisk" xlink:to="lab_us-gaap_ConcentrationRiskCreditRisk" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CostOfGoodsAndServicesSold_3473f232-11b5-47c5-a5a6-2c28d138b34b_terseLabel_en-US" xlink:label="lab_us-gaap_CostOfGoodsAndServicesSold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cost of goods sold</link:label>
    <link:label id="lab_us-gaap_CostOfGoodsAndServicesSold_label_en-US" xlink:label="lab_us-gaap_CostOfGoodsAndServicesSold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cost of Goods and Services Sold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostOfGoodsAndServicesSold" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CostOfGoodsAndServicesSold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CostOfGoodsAndServicesSold" xlink:to="lab_us-gaap_CostOfGoodsAndServicesSold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdvertisingCostsPolicyTextBlock_7179d83b-ce32-48a6-a8a1-5aa43ae51808_terseLabel_en-US" xlink:label="lab_us-gaap_AdvertisingCostsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Advertising</link:label>
    <link:label id="lab_us-gaap_AdvertisingCostsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_AdvertisingCostsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Advertising Cost [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdvertisingCostsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AdvertisingCostsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdvertisingCostsPolicyTextBlock" xlink:to="lab_us-gaap_AdvertisingCostsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAbstract_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashAndCashEquivalentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAbstract" xlink:to="lab_us-gaap_CashAndCashEquivalentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_98b2fab2-9dec-4d22-921a-5bedb80e9273_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of property and equipment</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:to="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodStockPriceTrigger_b78df930-9b57-4c47-b1dd-c4cb6d6aba88_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodStockPriceTrigger" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnout shares vesting requirement, weighted average price per share (in dollars per share)</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodStockPriceTrigger_label_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodStockPriceTrigger" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Contingent Consideration, Liability, Earnout Period, Stock Price Trigger</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodStockPriceTrigger" xlink:href="tlsi-20250331.xsd#tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodStockPriceTrigger"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodStockPriceTrigger" xlink:to="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodStockPriceTrigger" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PreferredStockNumberOfTradingDaysVolumeWeightedAveragePrice_6577a205-e380-4818-8868-90c68ceb9119_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockNumberOfTradingDaysVolumeWeightedAveragePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of trading days, VWAP</link:label>
    <link:label id="lab_tlsi_PreferredStockNumberOfTradingDaysVolumeWeightedAveragePrice_label_en-US" xlink:label="lab_tlsi_PreferredStockNumberOfTradingDaysVolumeWeightedAveragePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Number of Trading Days, Volume Weighted Average Price</link:label>
    <link:label id="lab_tlsi_PreferredStockNumberOfTradingDaysVolumeWeightedAveragePrice_documentation_en-US" xlink:label="lab_tlsi_PreferredStockNumberOfTradingDaysVolumeWeightedAveragePrice" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Stock, Number of Trading Days, Volume Weighted Average Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PreferredStockNumberOfTradingDaysVolumeWeightedAveragePrice" xlink:href="tlsi-20250331.xsd#tlsi_PreferredStockNumberOfTradingDaysVolumeWeightedAveragePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PreferredStockNumberOfTradingDaysVolumeWeightedAveragePrice" xlink:to="lab_tlsi_PreferredStockNumberOfTradingDaysVolumeWeightedAveragePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresTable_c1f097a9-92ac-4c75-b8d9-5a9db459e9e8_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosures [Table]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresTable"/>
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    <link:label id="lab_us-gaap_CommitmentsAndContingencies_6906a8bf-a523-4013-ad22-7a388d874455_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and contingencies</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingencies" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CommitmentsAndContingencies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingencies" xlink:to="lab_us-gaap_CommitmentsAndContingencies" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_2541e629-2993-4ce9-8170-a64e358f439a_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-Based Compensation</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:to="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_A2023PlanMember_3b499fd2-4d11-43a2-bb40-36d3aa8afc58_terseLabel_en-US" xlink:label="lab_tlsi_A2023PlanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2023 Plan</link:label>
    <link:label id="lab_tlsi_A2023PlanMember_label_en-US" xlink:label="lab_tlsi_A2023PlanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2023 Plan [Member]</link:label>
    <link:label id="lab_tlsi_A2023PlanMember_documentation_en-US" xlink:label="lab_tlsi_A2023PlanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2023 Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_A2023PlanMember" xlink:href="tlsi-20250331.xsd#tlsi_A2023PlanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_A2023PlanMember" xlink:to="lab_tlsi_A2023PlanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationsPolicy_109452cd-df49-49e4-97e8-c40181c6a4c8_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contingent Earnout Liability</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationsPolicy_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combinations Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_BusinessCombinationsPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationsPolicy" xlink:to="lab_us-gaap_BusinessCombinationsPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionTextBlock_9374cf7b-4846-412d-b63c-c4ab103681f6_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dynavax Purchase</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionTextBlock_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AssetAcquisitionTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionTextBlock" xlink:to="lab_us-gaap_AssetAcquisitionTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PrepaymentPremiumRatePeriodFourMember_7786e248-9adb-416d-b3dc-b08e5440f11e_terseLabel_en-US" xlink:label="lab_tlsi_PrepaymentPremiumRatePeriodFourMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">36 to 48 Months</link:label>
    <link:label id="lab_tlsi_PrepaymentPremiumRatePeriodFourMember_label_en-US" xlink:label="lab_tlsi_PrepaymentPremiumRatePeriodFourMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepayment Premium Rate, Period Four [Member]</link:label>
    <link:label id="lab_tlsi_PrepaymentPremiumRatePeriodFourMember_documentation_en-US" xlink:label="lab_tlsi_PrepaymentPremiumRatePeriodFourMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Prepayment Premium Rate, Period Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PrepaymentPremiumRatePeriodFourMember" xlink:href="tlsi-20250331.xsd#tlsi_PrepaymentPremiumRatePeriodFourMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PrepaymentPremiumRatePeriodFourMember" xlink:to="lab_tlsi_PrepaymentPremiumRatePeriodFourMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_CommercialMilestoneMember_562b3aaa-a14e-401c-91a7-81ab24d37a5c_terseLabel_en-US" xlink:label="lab_tlsi_CommercialMilestoneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial Milestone</link:label>
    <link:label id="lab_tlsi_CommercialMilestoneMember_label_en-US" xlink:label="lab_tlsi_CommercialMilestoneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Milestone [Member]</link:label>
    <link:label id="lab_tlsi_CommercialMilestoneMember_documentation_en-US" xlink:label="lab_tlsi_CommercialMilestoneMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commercial Milestone</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_CommercialMilestoneMember" xlink:href="tlsi-20250331.xsd#tlsi_CommercialMilestoneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_CommercialMilestoneMember" xlink:to="lab_tlsi_CommercialMilestoneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrTerminationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Termination Date</link:label>
    <link:label id="lab_ecd_TrdArrTerminationDate_label_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Termination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrTerminationDate" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_TrdArrTerminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrTerminationDate" xlink:to="lab_ecd_TrdArrTerminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightDomain_c4be0b5f-da73-4b4f-ae5f-2bf58dc31b7d_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfWarrantOrRightDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightDomain" xlink:to="lab_us-gaap_ClassOfWarrantOrRightDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationFirstReset_29c7fa1e-7299-4e46-8231-39c9de0ddf02_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationFirstReset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion price, first automatic reset</link:label>
    <link:label id="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationFirstReset_label_en-US" xlink:label="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationFirstReset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Conversion Price, Automatic Reset Duration, First Reset</link:label>
    <link:label id="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationFirstReset_documentation_en-US" xlink:label="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationFirstReset" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Stock, Conversion Price, Automatic Reset Duration, First Reset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PreferredStockConversionPriceAutomaticResetDurationFirstReset" xlink:href="tlsi-20250331.xsd#tlsi_PreferredStockConversionPriceAutomaticResetDurationFirstReset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PreferredStockConversionPriceAutomaticResetDurationFirstReset" xlink:to="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationFirstReset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NatureOfOperations_0a495751-7735-4021-ab6b-d82f533465f5_terseLabel_en-US" xlink:label="lab_us-gaap_NatureOfOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nature of Business</link:label>
    <link:label id="lab_us-gaap_NatureOfOperations_label_en-US" xlink:label="lab_us-gaap_NatureOfOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nature of Operations [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NatureOfOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NatureOfOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NatureOfOperations" xlink:to="lab_us-gaap_NatureOfOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_c7322532-9dab-48af-88da-7beb1aad574d_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise price of warrants (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Exercise Price of Warrants or Rights</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:to="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_78790929-b3a5-4b64-bf56-1ced0d63d839_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_SubsequentOrbiMedWarrantsEntityTwoMember_a2065a53-7d5b-4929-9be4-804b30254897_terseLabel_en-US" xlink:label="lab_tlsi_SubsequentOrbiMedWarrantsEntityTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent OrbiMed Warrants, Entity Two</link:label>
    <link:label id="lab_tlsi_SubsequentOrbiMedWarrantsEntityTwoMember_label_en-US" xlink:label="lab_tlsi_SubsequentOrbiMedWarrantsEntityTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent OrbiMed Warrants, Entity Two [Member]</link:label>
    <link:label id="lab_tlsi_SubsequentOrbiMedWarrantsEntityTwoMember_documentation_en-US" xlink:label="lab_tlsi_SubsequentOrbiMedWarrantsEntityTwoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Subsequent OrbiMed Warrants, Entity Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SubsequentOrbiMedWarrantsEntityTwoMember" xlink:href="tlsi-20250331.xsd#tlsi_SubsequentOrbiMedWarrantsEntityTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_SubsequentOrbiMedWarrantsEntityTwoMember" xlink:to="lab_tlsi_SubsequentOrbiMedWarrantsEntityTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_00fb2a5d-2273-43dd-9a18-3748c2052a47_terseLabel_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-Based Compensation</link:label>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:to="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_CommonStockSharePriceAverageDailyVolumeNumberOfTradingDays_9f6c3525-67c0-4a77-baa7-2d236f72bdf7_terseLabel_en-US" xlink:label="lab_tlsi_CommonStockSharePriceAverageDailyVolumeNumberOfTradingDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchase agreement, number of days used for measurement of average daily trading volume</link:label>
    <link:label id="lab_tlsi_CommonStockSharePriceAverageDailyVolumeNumberOfTradingDays_label_en-US" xlink:label="lab_tlsi_CommonStockSharePriceAverageDailyVolumeNumberOfTradingDays" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Share Price, Average Daily Volume, Number Of Trading Days</link:label>
    <link:label id="lab_tlsi_CommonStockSharePriceAverageDailyVolumeNumberOfTradingDays_documentation_en-US" xlink:label="lab_tlsi_CommonStockSharePriceAverageDailyVolumeNumberOfTradingDays" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock, Share Price, Average Daily Volume, Number Of Trading Days</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_CommonStockSharePriceAverageDailyVolumeNumberOfTradingDays" xlink:href="tlsi-20250331.xsd#tlsi_CommonStockSharePriceAverageDailyVolumeNumberOfTradingDays"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_CommonStockSharePriceAverageDailyVolumeNumberOfTradingDays" xlink:to="lab_tlsi_CommonStockSharePriceAverageDailyVolumeNumberOfTradingDays" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionConsiderationTransferred_7043640c-ec66-4186-b0e2-ab1e72cbcb59_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Upfront payment</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionConsiderationTransferred_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Consideration Transferred</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AssetAcquisitionConsiderationTransferred"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:to="lab_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_e8111639-c2dc-4c4d-a777-c30f1cfac4a1_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeLeasesPolicyTextBlock_6e387aea-a5b0-4752-9963-f7af42ffba26_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeLeasesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases</link:label>
    <link:label id="lab_us-gaap_LesseeLeasesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeLeasesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Leases [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeLeasesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeLeasesPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeLeasesPolicyTextBlock" xlink:to="lab_us-gaap_LesseeLeasesPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_dd7da607-13c1-46ef-96d6-50473666e3de_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentAxis" xlink:to="lab_us-gaap_DebtInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityTableTextBlock_14759f71-412c-4105-8c94-f93ee52afbad_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Convertible Preferred Stock</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_TemporaryEquityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityTableTextBlock" xlink:to="lab_us-gaap_TemporaryEquityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_d7fd4b4f-a393-4e3d-b1a1-2dd7de762f25_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net loss available to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_e1a7fdd1-02b9-42b8-8f14-41a46343b33b_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net loss</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_44197af9-2712-4d6e-afce-4995bc55318a_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net loss available to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TradingArrAxis_terseLabel_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangement:</link:label>
    <link:label id="lab_ecd_TradingArrAxis_label_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrAxis" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_TradingArrAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrAxis" xlink:to="lab_ecd_TradingArrAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ReverseRecapitalizationAbstract_label_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reverse Recapitalization [Abstract]</link:label>
    <link:label id="lab_tlsi_ReverseRecapitalizationAbstract_documentation_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reverse Recapitalization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ReverseRecapitalizationAbstract" xlink:href="tlsi-20250331.xsd#tlsi_ReverseRecapitalizationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ReverseRecapitalizationAbstract" xlink:to="lab_tlsi_ReverseRecapitalizationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfDebtDiscountPremium_95b338c8-637c-4349-813e-8de62300d337_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfDebtDiscountPremium" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-cash interest expense</link:label>
    <link:label id="lab_us-gaap_AmortizationOfDebtDiscountPremium_label_en-US" xlink:label="lab_us-gaap_AmortizationOfDebtDiscountPremium" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Debt Discount (Premium)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfDebtDiscountPremium" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AmortizationOfDebtDiscountPremium"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfDebtDiscountPremium" xlink:to="lab_us-gaap_AmortizationOfDebtDiscountPremium" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure, Table</link:label>
    <link:label id="lab_ecd_PvpTableTextBlock_label_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PvpTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTableTextBlock" xlink:to="lab_ecd_PvpTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_SaleOfStockNumberOfSharesToBeIssuedInTransaction_e55fe9ea-707e-486a-80ed-4084a328a096_terseLabel_en-US" xlink:label="lab_tlsi_SaleOfStockNumberOfSharesToBeIssuedInTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of stock, shares to be issued in transaction (in shares)</link:label>
    <link:label id="lab_tlsi_SaleOfStockNumberOfSharesToBeIssuedInTransaction_label_en-US" xlink:label="lab_tlsi_SaleOfStockNumberOfSharesToBeIssuedInTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale Of Stock, Number Of Shares To Be Issued In Transaction</link:label>
    <link:label id="lab_tlsi_SaleOfStockNumberOfSharesToBeIssuedInTransaction_documentation_en-US" xlink:label="lab_tlsi_SaleOfStockNumberOfSharesToBeIssuedInTransaction" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sale Of Stock, Number Of Shares To Be Issued In Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SaleOfStockNumberOfSharesToBeIssuedInTransaction" xlink:href="tlsi-20250331.xsd#tlsi_SaleOfStockNumberOfSharesToBeIssuedInTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_SaleOfStockNumberOfSharesToBeIssuedInTransaction" xlink:to="lab_tlsi_SaleOfStockNumberOfSharesToBeIssuedInTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in the Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:to="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year</link:label>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_label_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:to="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PaymentsForAssetAcquisitionMilestoneAmount_e8cfac2b-4076-4e71-ac8d-882bbf414ad6_terseLabel_en-US" xlink:label="lab_tlsi_PaymentsForAssetAcquisitionMilestoneAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payments for milestone</link:label>
    <link:label id="lab_tlsi_PaymentsForAssetAcquisitionMilestoneAmount_label_en-US" xlink:label="lab_tlsi_PaymentsForAssetAcquisitionMilestoneAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for Asset Acquisition, Milestone Amount</link:label>
    <link:label id="lab_tlsi_PaymentsForAssetAcquisitionMilestoneAmount_documentation_en-US" xlink:label="lab_tlsi_PaymentsForAssetAcquisitionMilestoneAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments for Asset Acquisition, Milestone Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PaymentsForAssetAcquisitionMilestoneAmount" xlink:href="tlsi-20250331.xsd#tlsi_PaymentsForAssetAcquisitionMilestoneAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PaymentsForAssetAcquisitionMilestoneAmount" xlink:to="lab_tlsi_PaymentsForAssetAcquisitionMilestoneAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFileNumber_363998bd-6478-4903-a45b-30f2c5f5f89a_terseLabel_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:label id="lab_dei_EntityFileNumber_label_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityFileNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFileNumber" xlink:to="lab_dei_EntityFileNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_da1baf9f-60fb-4f1c-9784-5a49741603c6_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalYearFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_DocumentFiscalYearFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalYearFocus" xlink:to="lab_dei_DocumentFiscalYearFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncomeStatementAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementAbstract" xlink:to="lab_us-gaap_IncomeStatementAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_0ffc5673-9a0c-4d01-8d74-a4c43d2c580f_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityAddressAddressLine1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_58d89679-2f8e-4d4a-b4b0-85c3e632a8ad_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentNameDomain" xlink:to="lab_us-gaap_DebtInstrumentNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAccruedLiabilitiesCurrent_1aefd8b7-303e-4b4c-a4b5-3bdafd71ee1f_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued liabilities - general</link:label>
    <link:label id="lab_us-gaap_OtherAccruedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Accrued Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_OtherAccruedLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:to="lab_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_ForgoneRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryIndName" xlink:to="lab_ecd_ForgoneRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_CommercialMilestoneTypeDomain_6e727ca3-7d0d-4ebe-8cbb-b3141717cca1_terseLabel_en-US" xlink:label="lab_tlsi_CommercialMilestoneTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial Milestone Type [Domain]</link:label>
    <link:label id="lab_tlsi_CommercialMilestoneTypeDomain_label_en-US" xlink:label="lab_tlsi_CommercialMilestoneTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Milestone Type [Domain]</link:label>
    <link:label id="lab_tlsi_CommercialMilestoneTypeDomain_documentation_en-US" xlink:label="lab_tlsi_CommercialMilestoneTypeDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commercial Milestone Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_CommercialMilestoneTypeDomain" xlink:href="tlsi-20250331.xsd#tlsi_CommercialMilestoneTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_CommercialMilestoneTypeDomain" xlink:to="lab_tlsi_CommercialMilestoneTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodDomain_c853c646-c45c-401d-81c5-fbad8c33db83_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Period [Domain]</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodDomain_label_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Period [Domain]</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodDomain_documentation_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Period [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentPeriodDomain" xlink:href="tlsi-20250331.xsd#tlsi_DerivativeInstrumentPeriodDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DerivativeInstrumentPeriodDomain" xlink:to="lab_tlsi_DerivativeInstrumentPeriodDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentPeriodEndDate_df8d8c51-eb3b-483b-9677-17b198e1a803_terseLabel_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:label id="lab_dei_DocumentPeriodEndDate_label_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_DocumentPeriodEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentPeriodEndDate" xlink:to="lab_dei_DocumentPeriodEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_SeriesAConvertiblePreferredStockMember_16561677-2a42-4f54-b6b6-47ac2d64927a_terseLabel_en-US" xlink:label="lab_tlsi_SeriesAConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series A Convertible Preferred Stock</link:label>
    <link:label id="lab_tlsi_SeriesAConvertiblePreferredStockMember_label_en-US" xlink:label="lab_tlsi_SeriesAConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series A Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_tlsi_SeriesAConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_tlsi_SeriesAConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series A Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SeriesAConvertiblePreferredStockMember" xlink:href="tlsi-20250331.xsd#tlsi_SeriesAConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_SeriesAConvertiblePreferredStockMember" xlink:to="lab_tlsi_SeriesAConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_622f07be-91f3-42e0-94a1-7d4dfd07065c_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_label_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_SubsidiarySaleOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:to="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_LeaseLiabilityCurrent_a3ba500d-faa2-49ec-acf8-f111923dc343_terseLabel_en-US" xlink:label="lab_tlsi_LeaseLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Short-term lease liabilities</link:label>
    <link:label id="lab_tlsi_LeaseLiabilityCurrent_label_en-US" xlink:label="lab_tlsi_LeaseLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease Liability, Current</link:label>
    <link:label id="lab_tlsi_LeaseLiabilityCurrent_documentation_en-US" xlink:label="lab_tlsi_LeaseLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lease Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_LeaseLiabilityCurrent" xlink:href="tlsi-20250331.xsd#tlsi_LeaseLiabilityCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_LeaseLiabilityCurrent" xlink:to="lab_tlsi_LeaseLiabilityCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_CommercialMilestoneTypeAxis_febf8a06-b370-4d41-9cb2-bb6122c57f8c_terseLabel_en-US" xlink:label="lab_tlsi_CommercialMilestoneTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial Milestone Type [Axis]</link:label>
    <link:label id="lab_tlsi_CommercialMilestoneTypeAxis_label_en-US" xlink:label="lab_tlsi_CommercialMilestoneTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Milestone Type [Axis]</link:label>
    <link:label id="lab_tlsi_CommercialMilestoneTypeAxis_documentation_en-US" xlink:label="lab_tlsi_CommercialMilestoneTypeAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commercial Milestone Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_CommercialMilestoneTypeAxis" xlink:href="tlsi-20250331.xsd#tlsi_CommercialMilestoneTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_CommercialMilestoneTypeAxis" xlink:to="lab_tlsi_CommercialMilestoneTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_UniversityOfTexasMDAndersonCancerCenterMember_27544424-c5b8-4b1b-a355-77308ed53844_terseLabel_en-US" xlink:label="lab_tlsi_UniversityOfTexasMDAndersonCancerCenterMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">University Of Texas MD Anderson Cancer Center</link:label>
    <link:label id="lab_tlsi_UniversityOfTexasMDAndersonCancerCenterMember_label_en-US" xlink:label="lab_tlsi_UniversityOfTexasMDAndersonCancerCenterMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">University Of Texas MD Anderson Cancer Center [Member]</link:label>
    <link:label id="lab_tlsi_UniversityOfTexasMDAndersonCancerCenterMember_documentation_en-US" xlink:label="lab_tlsi_UniversityOfTexasMDAndersonCancerCenterMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">University Of Texas MD Anderson Cancer Center</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_UniversityOfTexasMDAndersonCancerCenterMember" xlink:href="tlsi-20250331.xsd#tlsi_UniversityOfTexasMDAndersonCancerCenterMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_UniversityOfTexasMDAndersonCancerCenterMember" xlink:to="lab_tlsi_UniversityOfTexasMDAndersonCancerCenterMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryValuationReserves_caff60f6-2a75-4214-90e9-d36b0f5d7785_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_InventoryValuationReserves" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Reserve for obsolete inventory</link:label>
    <link:label id="lab_us-gaap_InventoryValuationReserves_label_en-US" xlink:label="lab_us-gaap_InventoryValuationReserves" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory Valuation Reserves</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryValuationReserves" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InventoryValuationReserves"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryValuationReserves" xlink:to="lab_us-gaap_InventoryValuationReserves" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AwardTmgMnpiCnsdrdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:to="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_6304e25b-b990-4199-9bfc-410b30390876_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rent payments</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingArrLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingArrLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Arrangements [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingArrLineItems" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_InsiderTradingArrLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingArrLineItems" xlink:to="lab_ecd_InsiderTradingArrLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsDisclosureTextBlock_6b31c5ca-8e4a-4385-b514-c860dc6b7f39_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalents and Restricted Cash</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_CashAndCashEquivalentsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsDisclosureTextBlock" xlink:to="lab_us-gaap_CashAndCashEquivalentsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_InventoryDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_InventoryDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryDisclosureAbstract" xlink:to="lab_us-gaap_InventoryDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingAggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_OutstandingAggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingAggtErrCompAmt" xlink:to="lab_ecd_OutstandingAggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdConsecutiveTradingDays_983d8d09-a210-4f3d-abe3-5af4adda2178_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnout period, threshold consecutive trading days</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdConsecutiveTradingDays_label_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Contingent Consideration, Liability, Earnout Period, Threshold Consecutive Trading Days</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdConsecutiveTradingDays_documentation_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Contingent Consideration, Liability, Earnout Period, Threshold Consecutive Trading Days</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdConsecutiveTradingDays" xlink:href="tlsi-20250331.xsd#tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdConsecutiveTradingDays"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdConsecutiveTradingDays" xlink:to="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdConsecutiveTradingDays" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodThreeMember_9db031eb-261e-40c2-b47e-5c4c67daf20a_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodThreeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tranche Three</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodThreeMember_label_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodThreeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Period Three [Member]</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodThreeMember_documentation_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodThreeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Period Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentPeriodThreeMember" xlink:href="tlsi-20250331.xsd#tlsi_DerivativeInstrumentPeriodThreeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DerivativeInstrumentPeriodThreeMember" xlink:to="lab_tlsi_DerivativeInstrumentPeriodThreeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_label_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoActuallyPaidCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PeoActuallyPaidCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoActuallyPaidCompAmt" xlink:to="lab_ecd_PeoActuallyPaidCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputSharePriceMember_df237f62-4b26-4e38-96db-7c174cf61361_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputSharePriceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current stock price</link:label>
    <link:label id="lab_us-gaap_MeasurementInputSharePriceMember_fed45e72-624d-413c-bec4-c7452d5986ad_verboseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputSharePriceMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Stock price</link:label>
    <link:label id="lab_us-gaap_MeasurementInputSharePriceMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputSharePriceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Share Price [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputSharePriceMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MeasurementInputSharePriceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputSharePriceMember" xlink:to="lab_us-gaap_MeasurementInputSharePriceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WarrantsAndRightsOutstanding_cc427024-b611-4d0a-b476-d4cf3e44b750_terseLabel_en-US" xlink:label="lab_us-gaap_WarrantsAndRightsOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding warrant liabilities</link:label>
    <link:label id="lab_us-gaap_WarrantsAndRightsOutstanding_label_en-US" xlink:label="lab_us-gaap_WarrantsAndRightsOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrants and Rights Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WarrantsAndRightsOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_WarrantsAndRightsOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WarrantsAndRightsOutstanding" xlink:to="lab_us-gaap_WarrantsAndRightsOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAxis_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation:</link:label>
    <link:label id="lab_ecd_AdjToCompAxis_label_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAxis" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AdjToCompAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAxis" xlink:to="lab_ecd_AdjToCompAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_MeasurementInputExpectedProbablyOfDrawsMember_26a17135-f92d-47de-86ba-1d1099df4f14_terseLabel_en-US" xlink:label="lab_tlsi_MeasurementInputExpectedProbablyOfDrawsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expected probability of draws</link:label>
    <link:label id="lab_tlsi_MeasurementInputExpectedProbablyOfDrawsMember_label_en-US" xlink:label="lab_tlsi_MeasurementInputExpectedProbablyOfDrawsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Expected Probably of Draws [Member]</link:label>
    <link:label id="lab_tlsi_MeasurementInputExpectedProbablyOfDrawsMember_documentation_en-US" xlink:label="lab_tlsi_MeasurementInputExpectedProbablyOfDrawsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Expected Probably of Draws</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_MeasurementInputExpectedProbablyOfDrawsMember" xlink:href="tlsi-20250331.xsd#tlsi_MeasurementInputExpectedProbablyOfDrawsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_MeasurementInputExpectedProbablyOfDrawsMember" xlink:to="lab_tlsi_MeasurementInputExpectedProbablyOfDrawsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentTransitionReport_5d9f6ad2-3cfc-4117-9cdd-ed71f306b50c_terseLabel_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:label id="lab_dei_DocumentTransitionReport_label_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentTransitionReport" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_DocumentTransitionReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentTransitionReport" xlink:to="lab_dei_DocumentTransitionReport" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentQuarterlyReport_3b8d622e-d5e0-4dc2-84f2-b488dee09de2_terseLabel_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:label id="lab_dei_DocumentQuarterlyReport_label_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentQuarterlyReport" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_DocumentQuarterlyReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentQuarterlyReport" xlink:to="lab_dei_DocumentQuarterlyReport" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_InitialOrbiMedWarrantSubstituteWarrantCertificateNumberOneMember_377253ad-f83f-4066-ad8d-9dabe6844bfc_terseLabel_en-US" xlink:label="lab_tlsi_InitialOrbiMedWarrantSubstituteWarrantCertificateNumberOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Initial OrbiMed Warrant, Substitute Warrant Certificate Number One</link:label>
    <link:label id="lab_tlsi_InitialOrbiMedWarrantSubstituteWarrantCertificateNumberOneMember_label_en-US" xlink:label="lab_tlsi_InitialOrbiMedWarrantSubstituteWarrantCertificateNumberOneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Initial OrbiMed Warrant, Substitute Warrant Certificate Number One [Member]</link:label>
    <link:label id="lab_tlsi_InitialOrbiMedWarrantSubstituteWarrantCertificateNumberOneMember_documentation_en-US" xlink:label="lab_tlsi_InitialOrbiMedWarrantSubstituteWarrantCertificateNumberOneMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Initial OrbiMed Warrant, Substitute Warrant Certificate Number One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_InitialOrbiMedWarrantSubstituteWarrantCertificateNumberOneMember" xlink:href="tlsi-20250331.xsd#tlsi_InitialOrbiMedWarrantSubstituteWarrantCertificateNumberOneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_InitialOrbiMedWarrantSubstituteWarrantCertificateNumberOneMember" xlink:to="lab_tlsi_InitialOrbiMedWarrantSubstituteWarrantCertificateNumberOneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_a728383f-b5a6-412c-85ca-b688b6f60cc5_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCurrentReportingStatus_6570be57-2d33-42d8-8372-310cbc97d623_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:label id="lab_dei_EntityCurrentReportingStatus_label_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCurrentReportingStatus" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityCurrentReportingStatus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCurrentReportingStatus" xlink:to="lab_dei_EntityCurrentReportingStatus" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodNetOfSharesReturned_22f4ae39-02e9-46fe-8281-ce145b5c226b_terseLabel_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodNetOfSharesReturned" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise of options (in shares)</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodNetOfSharesReturned_label_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodNetOfSharesReturned" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercises in Period, Net Of Shares Returned</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodNetOfSharesReturned_documentation_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodNetOfSharesReturned" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercises in Period, Net Of Shares Returned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodNetOfSharesReturned" xlink:href="tlsi-20250331.xsd#tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodNetOfSharesReturned"/>
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    <link:label id="lab_us-gaap_RetainedEarningsMember_1ab23879-3be7-4402-a3fb-5a3d25e64ec7_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated deficit</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsMember_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RetainedEarningsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsMember" xlink:to="lab_us-gaap_RetainedEarningsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PrepaymentPremiumRatePeriodAxis_b372a301-84b3-4f7f-95d7-b8b3fc52dc73_terseLabel_en-US" xlink:label="lab_tlsi_PrepaymentPremiumRatePeriodAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepayment Premium Rate, Period [Axis]</link:label>
    <link:label id="lab_tlsi_PrepaymentPremiumRatePeriodAxis_label_en-US" xlink:label="lab_tlsi_PrepaymentPremiumRatePeriodAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepayment Premium Rate, Period [Axis]</link:label>
    <link:label id="lab_tlsi_PrepaymentPremiumRatePeriodAxis_documentation_en-US" xlink:label="lab_tlsi_PrepaymentPremiumRatePeriodAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Prepayment Premium Rate, Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PrepaymentPremiumRatePeriodAxis" xlink:href="tlsi-20250331.xsd#tlsi_PrepaymentPremiumRatePeriodAxis"/>
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    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_bd2045ef-4db4-4ce2-bc26-e7ca9cf1caa3_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of debt issuance costs</link:label>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_label_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfFinancingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AmortizationOfFinancingCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfFinancingCosts" xlink:to="lab_us-gaap_AmortizationOfFinancingCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_PnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsSvcCstMember" xlink:to="lab_ecd_PnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionDomain_8d67e286-9661-4056-ad97-e943048592a9_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Domain]</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionDomain_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_AssetAcquisitionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionDomain" xlink:to="lab_us-gaap_AssetAcquisitionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_ce895a16-85dd-47ae-b801-82f30d973c20_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average common shares outstanding, basic (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method</link:label>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_label_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_StkPrcOrTsrEstimationMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:to="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputExercisePriceMember_b4775e54-772c-4778-b673-e9605da44e8c_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputExercisePriceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise price</link:label>
    <link:label id="lab_us-gaap_MeasurementInputExercisePriceMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputExercisePriceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Exercise Price [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputExercisePriceMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_MeasurementInputExercisePriceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputExercisePriceMember" xlink:to="lab_us-gaap_MeasurementInputExercisePriceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentInformationTable_d81f25b2-7889-4990-8f03-ca0fcee604e8_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Table]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationTable" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_DocumentInformationTable"/>
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    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_dc7f98e2-03da-4df3-ae5c-18ad0aafa0ec_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">RSUs</link:label>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_label_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock Units (RSUs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockUnitsRSUMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_RestrictedStockUnitsRSUMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedStockUnitsRSUMember" xlink:to="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementMember_a9ad55b4-a8db-4362-8928-0628d6e29b39_terseLabel_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Standby Equity Purchase Agreement</link:label>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementMember_label_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Standby Equity Purchase Agreement [Member]</link:label>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementMember_documentation_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Standby Equity Purchase Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_StandbyEquityPurchaseAgreementMember" xlink:href="tlsi-20250331.xsd#tlsi_StandbyEquityPurchaseAgreementMember"/>
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    <link:label id="lab_tlsi_FixedAssetPurchaseThroughExchangeOfFinanceLeaseRightOfUseAsset_6f91685c-57c9-4b51-815e-400e926583f3_terseLabel_en-US" xlink:label="lab_tlsi_FixedAssetPurchaseThroughExchangeOfFinanceLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed asset purchase through exchange of finance lease right-of-use asset</link:label>
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    <link:label id="lab_tlsi_FixedAssetPurchaseThroughExchangeOfFinanceLeaseRightOfUseAsset_documentation_en-US" xlink:label="lab_tlsi_FixedAssetPurchaseThroughExchangeOfFinanceLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Asset Purchase Through Exchange Of Finance Lease Right-Of-Use Asset</link:label>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_74d3cf6c-3665-46f1-876e-aec3e37c015c_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward"/>
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    <link:label id="lab_ecd_ExecutiveCategoryAxis_terseLabel_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Executive Category:</link:label>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_label_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Executive Category [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ExecutiveCategoryAxis" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_ExecutiveCategoryAxis"/>
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    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_AwardsCloseToMnpiDiscIndName"/>
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    <link:label id="lab_tlsi_AssetAcquisitionNumberOfCommercialMilestones_047589ba-6971-4224-bbec-91ffa0565dbb_terseLabel_en-US" xlink:label="lab_tlsi_AssetAcquisitionNumberOfCommercialMilestones" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of commercial milestones</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionNumberOfCommercialMilestones_label_en-US" xlink:label="lab_tlsi_AssetAcquisitionNumberOfCommercialMilestones" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Number of Commercial Milestones</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionNumberOfCommercialMilestones_documentation_en-US" xlink:label="lab_tlsi_AssetAcquisitionNumberOfCommercialMilestones" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Number of Commercial Milestones</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_AssetAcquisitionNumberOfCommercialMilestones" xlink:href="tlsi-20250331.xsd#tlsi_AssetAcquisitionNumberOfCommercialMilestones"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_AssetAcquisitionNumberOfCommercialMilestones" xlink:to="lab_tlsi_AssetAcquisitionNumberOfCommercialMilestones" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFilerCategory_c55f88e8-2bb0-4487-8584-0b64cdd7f1e5_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:label id="lab_dei_EntityFilerCategory_label_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityFilerCategory"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFilerCategory" xlink:to="lab_dei_EntityFilerCategory" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_WarrantsLiabilitiesTextBlock_0e67bd47-e9f1-47ff-9152-c441c65ecf81_terseLabel_en-US" xlink:label="lab_tlsi_WarrantsLiabilitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants</link:label>
    <link:label id="lab_tlsi_WarrantsLiabilitiesTextBlock_label_en-US" xlink:label="lab_tlsi_WarrantsLiabilitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrants Liabilities [Text Block]</link:label>
    <link:label id="lab_tlsi_WarrantsLiabilitiesTextBlock_documentation_en-US" xlink:label="lab_tlsi_WarrantsLiabilitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Warrants Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_WarrantsLiabilitiesTextBlock" xlink:href="tlsi-20250331.xsd#tlsi_WarrantsLiabilitiesTextBlock"/>
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    <link:label id="lab_tlsi_LoanFacilityDecember312025Member_7f60da2a-9235-4b43-8ba5-761000e70b42_terseLabel_en-US" xlink:label="lab_tlsi_LoanFacilityDecember312025Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan Facility, December 31, 2025</link:label>
    <link:label id="lab_tlsi_LoanFacilityDecember312025Member_label_en-US" xlink:label="lab_tlsi_LoanFacilityDecember312025Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan Facility, December 31, 2025 [Member]</link:label>
    <link:label id="lab_tlsi_LoanFacilityDecember312025Member_documentation_en-US" xlink:label="lab_tlsi_LoanFacilityDecember312025Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan Facility, December 31, 2025</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_LoanFacilityDecember312025Member" xlink:href="tlsi-20250331.xsd#tlsi_LoanFacilityDecember312025Member"/>
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    <link:label id="lab_ecd_CoSelectedMeasureName_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureName_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureName" xlink:href="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd#ecd_CoSelectedMeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureName" xlink:to="lab_ecd_CoSelectedMeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrivatePlacementMember_68fe89b4-b62f-49a6-9102-2559fb50e550_terseLabel_en-US" xlink:label="lab_us-gaap_PrivatePlacementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private Placement</link:label>
    <link:label id="lab_us-gaap_PrivatePlacementMember_label_en-US" xlink:label="lab_us-gaap_PrivatePlacementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Private Placement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrivatePlacementMember" xlink:href="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd#us-gaap_PrivatePlacementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrivatePlacementMember" xlink:to="lab_us-gaap_PrivatePlacementMember" xlink:type="arc" order="1"/>
  </link:labelLink>
</link:linkbase>
