Originally Posted by undeadcow
Too bad Lego Batman doesn't have iCloud backup with all the unlockables avaliable. I'd like to make room and resume it again later but hesitate in deleting. I still have Lego Batman on my device so can't speak specifically for that but typically deleting games in this fashion retains the Game Center information for that game for me. On my iPod I have noticed that if I'm offline when I make Game Center changes it doesn't synch when I do get online so maybe you are experiencing some connectivity issues (?).
No, the game center info is deleted by the game itself on deletion process, so no matter what option you select "KEEP" or "REMOVE", it will remove your game center info about the game.
I found a workaround is I need to TURN OFF WIFI/3G/LTE on my phone, then delete the game, now it cannot send remove action to the game center when I delete the game, then I can preserve my GC info about the game