There's no reason you couldn't rebase your feature branch work atop the commit it shares with the master branch, and push it. You would not be rewriting anything that the remote knows about.
Another option you might consider, if you need more flexibility, is doing your work in a branch off of your `feature-branch`, e.g., `feature-branch-wip`. When you're happy with your progress on `feature-branch-wip`, interactively rebase atop `feature-branch`, merge in, and push. Their process is satisfied, and they'll never be the wiser.
Another option you might consider, if you need more flexibility, is doing your work in a branch off of your `feature-branch`, e.g., `feature-branch-wip`. When you're happy with your progress on `feature-branch-wip`, interactively rebase atop `feature-branch`, merge in, and push. Their process is satisfied, and they'll never be the wiser.