I know what you mean, but I think that is something of a BGA bug in not realising an old message has already been "read". There is a way to make it go away - I think maybe clicking in the box to open the full chat and then minimising again? Not ideal, but workable. Tof would need to confirm, but it may not be something the extension can help with, as I don't think the extension would know if a message has been written while you were offline, and only receiving ones new while you're online would mean you miss things. Actually, there are times when I swear the chat doesn't show me messages which have been there for a few days (and my partner complains about this too - he says he never sees chat messages), so I suspect determining if messages are "new" or not is more than a bit bugged.
In any case, this probably needs to be addressed as a site bug report - I did try searching for one, and found a very old one that's basically closed but searching for bugs can be difficult (since your search only matches to a phrase, not individual terms AND'd).
In any case, this probably needs to be addressed as a site bug report - I did try searching for one, and found a very old one that's basically closed but searching for bugs can be difficult (since your search only matches to a phrase, not individual terms AND'd).