We're making a game that uses the Game Center leaderboards and achievements. After a game ends, we have a button that presents a GKGameCenterViewController when clicked. Is it OK to use the Game Center logo (the four colored balls) as an icon for the button? We've seen the logo used in this way for some other apps (e.g., Fruit Ninja), but we couldn't find a definitive answer as to whether this was generally allowed or whether some sort of special permission and/or licensing is required.
No one here can promise what app review will/won't accept/reject. App Review isn't here, and there are no pre-reviews.
My opinion is that you'll need to run the app review gauntlet to get an 'answer' that even smells definitive.
I don't believe any licensing is required. The use must be consistent with the intent of the trademark - the Game Center icon must send you to the Apple Game Center. When using other Apple Trademarks you must indicate the trademark with an ®. I'd add that to the icon.
You can ask them here:
https://www.apple.com/legal/contact/trademark-information.html
FWIW, we wound up not using the logo due to consistency with the app settings screen (where there's a Game Center achievement reset button but the regular GC logo color scheme looked inconsistent), so I never found out whether it would have passed review or not. We did write to legal, but we're probably too small for them to worry about and they never responded.