how do you permanently delete apps so that they no longer associated with an icloud account

New to Apple as my son wanted an iPhone and I'm trying to learn it to keep a safe watch out for him! Yikes! I have set parental controls that require permission to download apps but I just found that feature after he downloaded some apps that I am asking him to remove. He did remove them, but when he clicks on the app within the profile, it opens it up all over again. Is there a way to remove it permanently from his account?