The doorknob who had our TT before us hung a decoration on a wall with drywall screws that were longer than the wall was thick....
Screws were sticking out the wall on the outside.
When I pulled them out I just used some polymer based caulking a similar color and filled the holes, then smoothed it off on the outside and cleaned up any excess.
The thing to do is put the caulking tube nozzle right tight to the wall surface, then pump pressure on the gun for a second, then release the pressure before pulling the caulking gun away. This will force caulking right into the hole a ways so it isn't just on the surface.
