my game (Metrum) had github linked the entire time, but I removed it and put source code in downloads. Either way, it is available and I'm marked as no source code
Viewing post in but... source code?
Having just a link t a GitHub repository is fine, IMO it's the preferred way of distributing source code (or GitLab or Bitbucket or any repository). I like to checkout the source with Git, and maybe contribute fixes when relevant.
So you definitely don't need to remove the link to your GitHub project. Adding a ZIP of the source code in its jam state to itch.io is fine too.