<?xml version="1.0" encoding="utf-8"?>
<!--XBRL document created with Toppan Merrill Bridge  11.3.0.1 -->
<!--Based on XBRL 2.1-->
<!--Created on: 4/30/2026 9:19:49 AM-->
<!--Modified on: 4/30/2026 9:19:49 AM-->
<link:linkbase xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd" xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xbrldt="http://xbrl.org/2005/xbrldt" xmlns:xlink="http://www.w3.org/1999/xlink">
  <link:labelLink xlink:type="extended" xlink:role="http://www.xbrl.org/2003/role/link">
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CoverAbstract" xlink:label="dei_CoverAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_CoverAbstract" xlink:to="dei_CoverAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_CoverAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Document and Entity Information [Abstract]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentType" xlink:label="dei_DocumentType" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentType" xlink:to="dei_DocumentType_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_DocumentType_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Document Type</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityRegistrantName" xlink:label="dei_EntityRegistrantName" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityRegistrantName" xlink:to="dei_EntityRegistrantName_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityRegistrantName_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Entity Registrant Name</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityFilerCategory" xlink:label="dei_EntityFilerCategory" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityFilerCategory" xlink:to="dei_EntityFilerCategory_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityFilerCategory_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Entity Filer Category</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntitySmallBusiness" xlink:label="dei_EntitySmallBusiness" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntitySmallBusiness" xlink:to="dei_EntitySmallBusiness_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntitySmallBusiness_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Entity Small Business</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityEmergingGrowthCompany" xlink:label="dei_EntityEmergingGrowthCompany" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityEmergingGrowthCompany" xlink:to="dei_EntityEmergingGrowthCompany_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityEmergingGrowthCompany_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Entity Emerging Growth Company</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityExTransitionPeriod" xlink:label="dei_EntityExTransitionPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityExTransitionPeriod" xlink:to="dei_EntityExTransitionPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityExTransitionPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Entity Ex Transition Period</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCentralIndexKey" xlink:label="dei_EntityCentralIndexKey" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityCentralIndexKey" xlink:to="dei_EntityCentralIndexKey_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityCentralIndexKey_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Entity Central Index Key</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AmendmentFlag" xlink:label="dei_AmendmentFlag" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_AmendmentFlag" xlink:to="dei_AmendmentFlag_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_AmendmentFlag_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amendment Flag</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AmendmentDescription" xlink:label="dei_AmendmentDescription" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_AmendmentDescription" xlink:to="dei_AmendmentDescription_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_AmendmentDescription_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amendment Description</label>
    <loc xlink:type="locator" xlink:href="tmb-20260429.xsd#cgct_CgcIiiSponsorLlcMember" xlink:label="cgct_CgcIiiSponsorLlcMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cgct_CgcIiiSponsorLlcMember" xlink:to="cgct_CgcIiiSponsorLlcMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cgct_CgcIiiSponsorLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to CGC III Sponsor LLC.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cgct_CgcIiiSponsorLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CGC III Sponsor LLC [Member]</label>
    <loc xlink:type="locator" xlink:href="tmb-20260429.xsd#cgct_AffiliateOfCgcIiiSponsorLlcMember" xlink:label="cgct_AffiliateOfCgcIiiSponsorLlcMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cgct_AffiliateOfCgcIiiSponsorLlcMember" xlink:to="cgct_AffiliateOfCgcIiiSponsorLlcMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cgct_AffiliateOfCgcIiiSponsorLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to affiliate of CGC III Sponsor LLC.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cgct_AffiliateOfCgcIiiSponsorLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Affiliate of CGC III Sponsor LLC [Member]</label>
  </link:labelLink>
</link:linkbase>