Scratched the glossy black radio face, how to fix?

You may be out of luck.
Least risky...buy the finest mirco fiber towel you can and use Meguires Plastic Polish (I think it is # 9) not a swirl remover.
If that fails...remove the unit, remove the knobs and try machine polishing.
This is a touch screen and I am unsure if placing a darker tinted piece of plastic over the entire screen will still allow it to function and be readable.
Again, you may be out of luck and replacement will be the only fix.
Good luck...and let us know if you succeed.

 

Im having the same issue with my infotainment screen, did you get it fixed?

 

You could try Polywatch, which is used for getting scratches out of acrylic wristwatch crystals.

Search for it on YouTube and you can see the effect it has and decide if it's worth a go.

 

If you fix this, the next thing you should do is get a screen protector - available at ebay and amazon.

prius screen protector | eBay