So long as the file system is fixed, it should be straightforward to fix the git repository. I'm no git expert but maybe 'git repair' can deal with it; and if not then 'rm -rf' and 'git clone'.

To avoid silent corruption requires full metadata and data checksumming, ala Btrfs or ZFS. In those cases, not only is corruption unambiguously detected, but it's not allowed to propagate.