Rear mud flaps and the "extra screw"

To answer the OP and get out of the discussion of what that piece of plastic is called, and whether or not to remove the rear wheel:

I used an extra screw, because although it fit quite well, I could see that over the life of the car, it would wiggle a little, allow dirt and stuff in there, and eventually cause more wear, so I put in an extra screw. I used a self-tapping screw, so no nut on the other side. I first drilled a small hole so the screw wouldn't damage/crack the plastic, and it went in nicely and is very secure.

So, not entirely necessary, but I'm imagining this thing rattling around on my car for 100,000+ miles and decided it wouldn't hurt to secure it just a tiny bit more.