If you love your current partner, I dont see the reason why you should contact your ex. You also know that your current partner does not really like it for some reason, so why make things more complicated for both of you? Still, if you are in doubt there is no harm in asking your current one. You could tell her that it seems like your ex has started pestering you at the facebook, you dont know the reason and you want ask what she thinks about this subject?
But to keep things simple, I would ignore her for the moment, especially if its obvious that she has some intention to "make up" or something. Though there is no harm if she just want to be a friend again and your current one has no problem with it. But accidents can happen, so take care. Its all up to you though, these are all just outsiders POV.