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Gita predates the modern British imperial social construct of Caste, thus Gita has no mention of caste. However, Gita talks extensively about varna and gunas but that is not caste.
In Bhagawad Gita Lord Krishna says, “According to the three modes of material nature and the work ascribed to them, the four divisions of human society were created by Me.” (BG 4:13) Then He continues, “Brahmans, Kshatriyas, Vaishyas and Sudras are distinguished by their qualities of work in accordance with the modes of nature.” (BG 18:41)
It is important to observe that there is no mention of birth as a determining factor for one’s varna or classification. They are ascertained by their quality of work.
Lord Krishna adds, “By following his qualities of work, every man can become perfect… By worship of the Lord, who is the source of all beings and who is all-pervading, man can, in the performance of his own duty [or occupation], attain perfection.” (BG 18:45-46).
Forced designation or untouchability was never a part of the Vedic process.
Source: https://www.stephen-knapp.com/casteism.htm
Other reading material: https://www.hinduamerican.org/all-about-caste
Relevant videos:
Contributor: Dilip Amin
Location of this page (25b): https://www.hinduspeakers.org/ufaqs/what-does-gita-say-about-the-caste-system/
Category:
25. Caste System