Yep delete the markup!
If actually you have more specific requirements then state exactly what you are needing to do.
By delete the markup, I assume you mean delete it from the template files. Or, less efficiently, I could use CSS to not display the avatar.
But when I say disable group avatars, I am also thinking about cutting off the group creation step where people can upload avatars, and remove avatar tab from group edit screen…
check the various templates files you can do a fair amount of that , removing the tab may be harder, can’t recall how that’s implemented but the template file will clue you in.
Visually disabling via CSS isn’t really the best approach though as it’s client side and easily overridden.
