Hey markescia,
Thanks for using Apple Support Communities. I see that you’re having trouble accessing GamePigeon from your iMessage app and I’d like to help.
I suggest that you try deleting the GamePigeon app from your iMessage and then reinstall it. To do this, open up your iMessage app > select the ‘App Store’ icon > scroll all the way to the right side until you see the icon with three dots > select that icon and you’ll be able to view all your ‘Favorites’ and list of apps that’s currently installed.
Locate the PigeonGame app and swipe to the left to view the ‘Delete’ option. Once deleted, go back to the App Store for your iMessage and reinstall the game. Use this resource for guidance: Use iMessage apps on your iPhone, iPad, and iPod touch
I hope this helps! Have a great day!