This guide is especially helpful for people that had 100 games, now only have 10, and wish the other 90 could disappear from GameCenter, and not just by "removing" game data when you deleted the app.
Hold down the app and choose the game that you want to delete. I'll be deleting "Spider", as in Spider Solitaire.
Press Delete (obviously).
Press Remove. Don't even think of pressing Keep.
Tada! Spider solitaire is gone! Oops, that didn't go as planned...Just a second, everyone.
That's only the first half of the deletion. Next, if you have GameCenter in your Multitasking Tray, remove it. Note: Double click the home button, then hold down the app (for all the non-techies).
Go into WiFi. And no, my WiFi is not named iPod touch.
Go into GameCenter. You've been hearing about it, but now you actually get to access it. -sniffling- "Sorry, this is such a special moment."
And, voila! Spider be gone! By the way, might I add, it's much more effective than getting a plastic cup, capturing your iPhone (or iPod or iPad), and placing it outside. Yeah, I'm looking at you.
You just learned how to TRULY delete GameCenter data. Now, wasn't that satisfying? If it was, give yourself a high five. If it wasn't...you can leave now.
You can turn WiFi back on now.😉