Clean disc with Tooth paste or Window cleaner or Brasso or a scratch repair kit. That might work.

Circle scratch sucks I bought a second hand game once with that and it only works if I insert the game disc in a certain way. Most of the time, the game freezes on the game loading screen.

Game stores have disc scratch removing machines that could remove the scratch and hopefully not break the disc.

Being a rental store you could return the game and I bet they would not be smart enough to check the disc to see if it works or not.

Never move a XBox 360 with a game disc in it while it is operating. Moving it from horizontal to vertical or vice versa will scratch the game discs.

Ahhh that sucks. The only time I had a disc scratch from my Xbox was when we first got it, and had it standing straight up. I was kicking a volleyball around the house and I hit over the Xbox. Needless to say it scratched the crap out of my brother and my Top Spin 2 game. It was rubbish anyways, and it was preowned.