Thank you, I'll check that out, to be sure.

Do you know if it is possible to just restore the mail from the time machine, that way only altering the last week or so that has not been backed up, but also has not been removed from the server?

I did, by the way, go onto the server and deleted the offending emails from it, so they should not show back up.

I just thought of another peculiar behavior these emails had. If you highlighted them in the list, (and this is before opening them, because usually these things are discarded without even being opened) they immediately showed up as opened (you know, no more blue dot) as the message that the ######.emlx did not exist etc. etc.