How to "Message" Group Member Who is not a "Friend"?

I maintain a private group (old) for my school alumni association. People who attended or graduated from the school are welcome to "Join". I do not know most of these people personally so I don't "Friend" them. When they do ask to "Join", I check the alumni database to see if they actually did attend the school. Occasionally, there will be someone who is not in the alumni database and I need to question them as to why they are not in the database. If I try to "Message" them, I can't because they are not a "Friend". If I accept their "Request to Join" and they are now shown on the "Member List", I still can't "Message" them. The only way I can see to handle this is to "Remove" them from the group and hope they send me an email complaining about why they where rejected. Is there any other way to handle this situation?

I didn't quite understand your issue, but if they set their messaging settings to 'Everyone', you should be able to contact them directly.

If they have set their Privacy to receive messages only from Friends even though they have requested to Join my group, then I cannot message them, right?