Hey Timothy Stringer,
Thanks for using Apple Support Communities! I understand you have some questions about the "recent" option in the iMessage App drawer. I am happy to provide some information to help.
You can definitely edit the app drawer but adding and removing apps, or rearranging them as well. There isn't an option to edit the content in "recents" this is automatically curated and will include what you're seeing, along with Memoji stickers if you're using those as well. You can see more about that here: Use iMessage apps on your iPhone, iPad, and iPod touch
Thanks again, and have a great day!