well, I couldn't do the poll.. to open ended.
I would explain basically what you explained here. Say that by the looks of it, it is a neglectful situation. Explain that you can call animal control and she can pay the consequences there, (I was thinking mention what would happen to the puppy but it seems like that might not even matter..) or say surrender the dog to you, without paying, and let her know she honestly wins this way. refuse to pay for the dog, tell her she will end up paying herself and really be in trouble then. If the puppy is physically suffering, its only fair to take the dog and pay for its sake, but try to work around the situation first. At least, this is what I would do. Good luck, and hope to hear good news!