I had the same problem.
As a Git-newbie, I thought it was complete FUBAR.
Solution: Somewhat like @bara suggested + created a local backup branch
# Rewind to commit just before the pushed-and-amended one.
# Replace <hash> with the needed hash.
# --soft means: leave all the changes there, so nothing is lost.
git reset --soft <hash>
# Create new branch, just for a backup, still having all changes in it.
# The branch was feature/1234, new one - feature/1234-gone-bad
git checkout -b feature/1234-gone-bad
# Commit all the changes (all the mess) not to lose it & not to carry around
git commit -a -m "feature/1234 backup"
# Switch back to the original branch
git checkout feature/1234
# Pull the from remote (named 'origin'), thus 'repairing' our main problem
git pull origin/feature/1234
# Now you have a clean-and-non-diverged branch and a backup of the local changes.
# Check the needed files from the backup branch
git checkout feature/1234-gone-bad -- the/path/to/file.php
Maybe it's not a fast and clean solution, and I lost my history (1 commit instead of 5), but it saved a day's work.