plastic window on my car cover eating my clearcoat?

[firulice]

I recently purchased a 40th anniversary outdoor car cover from a member on here in like new condition. I put it on for the first time last week and took it off today for the first time so it's been almost a week on the car. then today where that plastic window was sitting just above the license plate and under the hatch lid I noticed some marks in my paint. upon closer inspection it looks like those spots were from where the plastic was touching the clear coat and it had eaten through? I tried some quick detailer, no help. Then some goo gone...nada. I then tried some Meguiars ScratchX and with some work it made it better but not perfect. I worked on that for a while and then I clay barred the spots and waxed over the top. it looks better now but if you look really close you can still tell the little ripple marks where the plastic was touching the car. I have never seen or heard anything like this? The plastic looks brand new on the cover and is clear and has no residue on it. The car sits in a garage undisturbed and out of any extreme temps. thoughts?

I know I should have taken pictures but I was freaking out and wanted to get it fixed quickly