If you use Game Center to play a lot of multiplayer games, you may start accumulating a lot of friends. If you start getting too many requests or just want to clean up your Game Center friends list a little, it's actually a pretty easy task.
Launch the Game Center app from the Home screen of your iPhone or iPad.
Tap on the Friends tab in the bottom navigation menu.
Find the friend in the list that you'd like to remove and swipe sideways on their name.
You'll notice an Unfriend button appear. Tap on it.
That's all there is to it. That person will no longer appear in your Game Center friends list and won't be able to send you game requests any longer.