Write-only git repository?

I have a situation where it would be really useful to have a "dropbox" git repository. That is, a repo that can be pushed to but not cloned or pulled from. None of the git server solutions that I have looked at (gogs, Gitlab, Atlassian Bitbucket) offer such a thing. Is there another one that I've missed? Is it even possible to have such a thing as a write-only repo? I suspect it may not be, but I haven't looked into the git push/pull protocol in detail (yet).