Reddit mentions of Displex Display Polish

If the scratches aren't too deep, you will likely have better luck with a subtractive product like Polywatch or Displex.

If any of the scratches are too deep to buff out with those, do your best, then fill the cracks with Vaseline and put a screen protector over it.

I had a large scratch in the center of my screen, I used displex to fix it. It worked great, http://www.amazon.com/Displex-00300-Display-Polish/dp/B00CFLMIFC

I used Displex to remove the scratches on mine (yes, it really worked...I'm not a shill for this or any product).
http://www.amazon.com/gp/product/B00CFLMIFC/ref=oh_aui_detailpage_o06_s01?ie=UTF8&psc=1

Once I got the scratches out, I put 41mm Klearkare protectors on the lenses. Follow the application instructions to the letter and worry about scratches no more. (There are two in a package.)
http://www.amazon.com/gp/product/B00BUJ39ZI/ref=oh_aui_detailpage_o07_s00?ie=UTF8&psc=1

I'm sure there are other solutions, but this worked well for me.

Toothpaste might kinda work on the disc, but if you're going to send it in for replacement and it costs more than $10 you might want to give this stuff a shot: http://www.amazon.com/Displex-00300-Display-Polish/dp/B00CFLMIFC

It's used for removing scratches from plastic displays, it's basically just a polish. Worth a shot

They're plastic right? Try some displex: http://www.amazon.com/Displex-00300-Display-Polish/dp/B00CFLMIFC