disable app store in imessage

I have pretty much everything disabled on my child’s phone. I do not want them on the internet at all. I just want them to call or text me and have access to some apps that they need for work and location. I have the restrictions all set up and everything. But then while going through the iMessage app I noticed there are 2 options I can’t delete from the app drawer (when you select the “A” icon to view app shortcuts): the photos app and the App Store app. I CANNOT find a way to delete or disable the App Store one. Even if the App Store is disabled on the phone, you can still access it through iMessage. Seems like a huge oversight and an easy way for kids to browse the “internet” on a device that’s supposed to be completely locked