Hello LRank218,
Thank you for using Apple Support Communities.
I understand that you would like to limit access to games, specifically the GamePigeon app, on your stepson's iPhone. Since that app isn't specifically addressed by Screen Time. That being said, I have a couple of thoughts that might address what you want to do. You can try restricting Game Center, specifically multiplayer games. You can limit his usage time of other apps. As a last restort, you can either delete or offload the GamePigeon app from the iPhone. You can use this support article for information on these actions:
Use parental controls on your child's iPhone, iPad, and iPod touch
As a last restort, you can either delete or offload the GamePigeon app from the iPhone. This is mentioned in the following support article:
How to check the storage on your iPhone, iPad, and iPod touch
Specifically this:
"Go to Settings > General > [Device] Storage. You might see a list of recommendations for optimizing your device's storage, followed by a list of installed apps and the amount of storage each one uses. Tap an app's name for more information about its storage. Cached data and temporary data might not be counted as usage.
In the detailed view you can:
- Offload the app, which frees up storage used by the app, but keeps its documents and data.
- Delete the app, which removes the app and its related data.
- Depending on the app, you might be able to delete some of its documents and data."
As it mentions, Offloading the app will remove the app, but will not delete the associated documents and data. This way, by blocking his downloading of apps, he cannot download it again. But when he is no longer grounded, you can authorize him to download the app again.
Best regards.