You can log out of Game Center in iOS 7 by following these steps:
1. Navigate to Settings > Game Center
2. Tap the "Apple ID" tab
3. Tap "Sign Out" on the pop up box
Logging out of Game Center will eliminate the "Welcome back..." banner, but the banner will be replaced by an equally annoying sign in screen that will also interrupt game play and increase a game's loading time. You can learn how to disable the "Welcome back..." banner on jailbroken devices here.