You can try a hairdryer or heat gun, or a magic sponge (mr clean eraser, etc) or other gentle abrasive method (which can make it worse, try in a tiny less conspicuous area first), or detailing goop to wet it, Armor All, etc.
I think the best you can realistically do is clean it to get the big rough parts or transfer off, then either magic erase it like Dave9 said, followed by putting some kind of interior shine or oil-protectant on it to fill the roughness and make it less visible. Kind of like waxing the car.
Those scratches are still going to be there, the bell can't be unrung unfortunately.
I've had very good luck putting interior shine on large white splotches on black plastic and they're completely invisible.
Maybe some aftermarket covers to hide those marks. From the pictures, you've gone through the plastic outer layer. That won't hide with any type of spray.