You don't have to do that. I'm kinda leaning into what @eyeball kid said, just roll with the scratches. It's just annoying as I've only had it a couple of weeks!I have some dead mods that have defeated me and cannot fix (dead internal cells) so I will deliberately scratch a screen and test it for you, but I did try the toothpaste on a CD, didn't work for me, though these are a softer plastic, problem will be how deep the scratches are.
I will also try car scratch remover.