My team is working with two remotes: origin and backup.
backup is GitHub-based, so it does not support large files. Someone made a commit to origin with a large file and since then we have all made numerous commits. 
We have since deleted that large file. (In fact, I didn't finish pulling the commit with it and I don't think I actually downloaded it because  it was removed in the succeeding commit.)
I have tried
git checkout master
git checkout --orphan tmp
git commit -m "Root"
git push backup master
but the push fails due to that large file exceeding the size limit.
How do I push the current state of origin to backup but not the large file?