Hi,
I think you can get rid of the notifications if you mark all the messages read...
Click the box, at the right, on the row at the top which says 'Private Messages in Folder: Inbox' and then all the messages on the screen will be selected.
Then go down to the last message, and below it says 'Selected Messages: Move to Folder'. Change that to 'Mark as read' or 'Delete' and click 'Go'.