The point of that group is that it's pretty much automated. When people hit the required number of posts they drop out of it automatically. It doesn't really need any active involvement.
Not when you want people to remain on the moderated list until they are know not to be a idiot. So the automated count doesn't help in this case. Just it be easier if moderators can have access to that rather than just admins.
You can go into Manage groups and edit the Newly Registered Users group.
Checkmark "Exempt group leader from permissions"
Add your moderators to the Registered Users group as group leaders. Then they can remove the users from their UCP on their Groups tab.
If you give your moderators admin permissions for usergroups then they will be able to add or delete anyone from any group, or even create new groups if they want. If you give them Manage Users permissions they will be able to do alot more than just delete them from a group.
You are better-off just making them a Group Leader as I explained.