How to remove screw anchors from wall?
If the wall is standard drywall, I would use a punch, wooden dowel or something similar and push them in. By design they are resistant to pulling out with out some wall damage. They just need to be slightly below the surface. Repairing the holes will depend on the wall finish. If it is painted then spackle as @Craig suggested, and repaint. If it has wallpaper with and intricate pattern you can try to use small pieces (providing you have some extra) cut with a paper hole puncher and glued in place.