Hmmm, that's a shame. But it almost looks like the damage is to a raised case edge, because your phone looks white, and it looks (to me) like you have a blue case wrapping around a white GS3. I guess I didn't realize that the white GS3 has such at dark bezel border. Must be an optical illusion.
Does AT&T care if you replace that GS3 with another one, on your own? I'm not sure. But if that's ok, and you can afford to buy a new one on sale, you could list this one on eBay & on your local Craigslist, perhaps also on Gazelle & NextWorth, etc.?(AWTTW? first, be sure to thoroughly research current selling prices & bids for phones in similar conditions as yours), and then when it sells ? you could just go out and get another GS3 on one of those $49. or $99. deals, that seem to be offered bi-monthly, every two weeks or so.