If you want to rewrite all commits in branch just:

git filter-branch --commit-filter '
  if [ "$GIT_AUTHOR_EMAIL" = "invalid-email@example.com" ];
  then
          GIT_AUTHOR_EMAIL="valid-email@example.com";
          git commit-tree "$@";
  else
          git commit-tree "$@";
  fi' HEAD

If you want to rewrite some commits in history just:

git rebase -i some-commit-hash

Then, mark as edit/e commits with invalid email. Save and exit from editor.

Repeat this command for all commits marked as edit/e.

git commit --amend --author="User Name <valid-email@example.com>" --no-edit
git rebase --continue