By default the limited administrator has Full access to every group, When restricting access to groups from a limited administrator, changing the access right on a per group basis can become very tedious.

• Right-click on the "My Company" group
• Select "Set No Access to this group and all subgroups" or "Set Read-only Access to this group and all subgroups". 
• Set the required Access Rights to the groups that this limited admin will manage.