What do you make of this move?

No this doesn't seem odd. She's obviously still attracted to you. She only broke up with you so she can be more dependent so you say, so its not weird at all for her to still want to hook up on occasion. If you don't have a problem with it then I would go for it. Just realize that it doesn't mean you guys are back together. If you're not ready then just tell her that. She'll understand and quit pestering you for a