Looks like a standard wood screw - shouldn't have any nuts that will drop behind. There really isn't much "behind" the panels - they are basically just solid plywood sheets.
After you take the screw out - you can plug the hole with a dowel & stain it to match.
The other holes to patch are going to be at the vinyl clad ceiling & walls - those are best patched by just putting a rivet in them - then leaving them aluminum or finding a paint that matches the vinyl wallcovering.
Shari