Also is the notes.id file they use at home, exactly the same as the id file version at work? Domino unread marks are notorious for problems, with "fix all solutions" like marking all of the documents as read to reset the unread marks table, and it will work for a while until it gets out of sync again.
Alternatively, if they have a local replica on the home PC, have them select both icons on the workspace, and do an Edit | Unread Marks | Exchange Unread marks.
If your Domino environment is Clustered, see also IBM Technote 1159331
IBM - Documents marked read from BlackBerry later appear unread in the Notes client