The anchors are simple plastic plugs. They spun when you removed the screws, and are no longer effective, since they no longer grip the soft interior of the drywall. Try coating them with white glue and reinserting them in the holes. Just push them flush with the surface, by hand, or lightly tap with a hammer, if needed. Wait a day and reinstall the grill. If this fails, take a screw to Lowes and find the anchor display. You are looking for a white plastic anchor that looks like curly pasta. Find the ones that match you screw size. These are installed with a phillips head screwdriver and just get screwed into the existing holes by hand. A common brand is "E-Z Anchor" Good luck, you will successfully conquer this one.