Docker source isn't public right now. Lot's of dev rearchitecting for next release. However, you can see the entrypoint for GitHub here:
https://github.com/touchlab/gp-check. There's nothing specific to GitHub once you call into the Docker image. Just she ssh key that gives access to the KMP repo. Not sure how GitLab does that. In GitHub, you use "deploy keys". For that you need an ssh key.