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 ...
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.