Hello, Mike2021C. Thank you for posting to the Apple Support Communities. You’ve come to the right place to ask for help with your iPad. We understand the situation and how you are noticing a Game Center message each time you load up a game on your device. We’re happy to see what we can do to clear this message away.
To get started on this, there are some initial troubleshooting steps we’d suggest trying first. It may be helpful to restart your device before installing any available App Store updates. The following two Apple Support articles explain how you can complete these steps:
Restart your iPad - Apple Support
How to manually update apps on your Apple device - Apple Support
If you continue to notice the same message after completing the steps above, we can help you more. To continue, please try to sign out, and then back in to your Game Center account. You can do this right from the Settings app on your device. Find out more in this last article:
Use Game Center to play with friends - Apple Support
We hope that these steps allow you to get back to enjoying Game Center without seeing this message each time. Please let us know if you have any other questions about this topic.
Cheers!