1) Back-up your iOS device using iTunes
Here are instructions from the Apple site that will walk you through the back-up/restore process in more detail.
Note: this is not the same as simply Syncing with iTunes. Backing up is an extra step to take.
2) Delete the game from your device it may also ask if you want to keep your GameCenter data, feel free to say Yes
3) Then 'restore from backup' using iTunes (see link above)