Try doing a clean git clone in TeamCity. Nope, not even with the plugins that claim “clean clone” capability. You should be confident that CI can build/run/test an app with a clean starting point. If the CI forces a cached state on an agent that you can’t clear… TeamCity just does it wrong.
You just check the "delete files in checkout directory" box in the run screen. Are you thinking of something different? I've never had trouble doing a clean clone.
It’s been a while since I used it but I do remember that it doesn’t do a clean checkout and you can’t force it to. It leaves artifacts on the agent that can interfere with subsequent builds. I assume they do it for speed but it can affect reliability of builds