I figured it out and it is a little bug even if working as designed.  Basically, Webex Chat seems to hold onto the unread status of messages even when the message has been purged.  I had noticed green dots next to some names before but when I checked...

That is a sound concept, but it does not work.  I suspect there is a bug somewhere as there is no quick way to clear this number.  For example, I just reset my Webex Chat and signed back in.  Before the reset, it was showing 6 unread messages next to...