I did this for coloradok5 recently, or at least something very similar. The second part of
this post describes how to only allow users from one group to add avatars to their profile. Just use that and remove all current avatars with this SQL command:
UPDATE w3t_Users SET U_Picture = ''
Of course, it is quite easy to edit the profile page, and showthreaded/showflat to only show the avatar if they are of the specified group, but that would require more changes.
I'm not sure if I should add those two little hacks as mods, they aren't much to show, but maybe it would be easier to find.