How can I repair drywall after removing tile?
I'm sure that there will be a lot of surface damage to the backer. Was it sheetrock of cement board?  Regardless, remove as much of the old thinset and grout as possible, even it it gouges into the backer a bit.  You can refinish the backer with a first coat of setting type drywall compound, or regular general purpose drywall compound. Try to use the widest knife possible to apply the compound to minimize the trails.  Knife or sand down any real high spots after the first coat dries.  If you want a smooth finish surface, mix some GP compound with a little bit of water and a small amount of Ivory dish soap, mix well.  Again, apply with a wide knife, let dry and sand.  Touch up any flaw areas with this same mixture and finish sand.  Be sure to prime the new mud finish with a PVA drywall sealer/primer, then paint as you wish.  Good Luck