I have set a ‘Users Group’ in my access and delegation preferences with only access to ‘Read any Calendar Entry and To Do or Contact’ but clients in this group can still read mail documents.
Subject: Do they only see emails relating to calendar?
Use the workstation of one of the people in that group, open your mail file, and check to see if all of the “mail” they see in the inbox is relating to calendar (invitations to meetings, accepts and declines, etc.). If they are, you may want to set your Calendar display preference to move those items out of the inbox after dealing with them.