At least it's on the slab and not the coin. You may be able to remove the damage or at least lighten it up a bit.
Try some 91% rubbing alcohol (isopropanol) on those. Won't hurt the plastic but might clean off the schmutz.
If I recall correctly, high percentage isopropyl alcohol WILL affect plastic. I think I made that mistake once.
I found the Turtle Wax lens restorer at Walmart this evening and gave it a shot. I only had time to try it on the obverse, but here are the results I obtained. As hard as I tried, I made no progress on the scratches toward the top of the coin. Overall, I think it did a decent job. Before After
@messydesk, this will have to wait until next time. My wife looked on in bewilderment as I searched the house for something to use. I am pretty sure she thinks I have finally lost my mind.
You could use light cooking oil in a pinch. Your wife already thinks you're nuts, so what have you got to lose?
Alcohols are miserable solvents for pretty much any plastic. Could try it on a corner first though...