How do I permanently delete data from a game when I delete it from my iPhone/ipad

Solution 1:

If the game is saving game data via iCloud, the data might have not been deleted when you removed the app from your iOS device.

Go to Settings > General > Usage

There will be a section called iCloud with a Manage Storage option. Tapping this will load all your data stored on iCloud.

Under the Documents & Data section, check to see if your game has data saved to iCloud. If it does, simply tap on it and tap on the edit button in the top right hand corner to bring up the Delete prompt.

Solution 2:

In iOS 8, just go to Game Center app > Games > swipe left on games you want to remove and tap the button.