Sigh... Seems like it is chemically stained and cannot be removed by simply wiping. Have you tried OPC? Anyways, if still cannnot, what you should do is 3 easy steps:
1. Make sure whether your side mirror is glass or plastic made.
2. Polish it off with the appropriate product i.e plastic polish if plastic, rubbing compound if glass.
3. Go back to the shop and fk the workers.