Here don’t push --force to .git which will delete your history. But here is a tip to recover from the situation after you have pushed out the amended commit with --force.
Use git reflog to find the old commit that you amended
Create a merge between old and new, using git checkout new && git merge -s ours old.
Merge that to your master with git merge master
Update your master with the result with git push . HEAD:master
Push the result out.
So their later merges will not see the conflicts between old and new that resulted from your amending.