The agreement Jones had with the mother is with the mother. It excuses Jones from any legal and moral obligation he has to her as a co-parent. It does not satisfies his moral obligations as the father to the child.

As a society we tend not to recognize that children have any kind of legal right to parental affection, but its pretty clear that Jones has opted not to fulfill that moral duty. He has given what amounts to pocket change to this girls mother, but no amount of money can substitute for not having a father.

Legally the woman cannot demand anything on the basis of that, but morally I'm all for her taking Jones for a ride. Fuck the guy. When you bastardize your own children, you are the bastard.