What is the quickest way to remove material scraped onto a car's paintwork from another car's plastic wingmirror? Removing even a small amount is so far taking a large amount of elbow grease.
Standard automotive repair practice is to use polishing compound for light-to-moderate finish removal, and rubbing compound for rapid, heavy removal of material; these can be found at most auto supply stores and even supermarkets, as well as online.
Be aware you're removing a bit of the auto's finish, as well as the transferred paint:
Do not remove too much paint, i.e. go down to primer, or major repainting will be needed.
After cleanup, apply a good paste wax to protect the area where paint was removed and to restore gloss.