Telsaunread is a plugin for NOVA launcher that allows for an unread count next to various messaging programs, email, SMS, etc. it does not have an option in any menus for Facebook. But, disabling that feature in NOVA clearly removes the unread count (which I personally really like).
I am also running nova on a stock nexus 7 and do not get the notifier there.
So, this is definitely coming from Samsung.
It can be disabled with tesla unread, which suggests there should be other ways to do it too.
I doubt there is an option in Facebook though. It is coming from the OS.