I actually don't mind answering curious questions when I'm out with my baby for her walks. I know I'm always curious myself especially when I was looking to buying one. If possible, I'd have wanted to buy from a breeder who's been proven by a healthy sweet yorkie I fell in love with in person where the owner of said sweet yorkie vouches for the health and temperament of her dog. And of course, price is important to me too because I don't want to get my hopes up if it's at a range I couldn't justify spending. At that point, knowing where they got their dog from may or may not matter anymore except to note that said breeder probably breeds healthy dogs I cannot bring myself to buying. Good to know to refer to another who doesn't question the cost of living and loving around here.
Problem here is, this woman does seem highly suspicious if not also very lacking in manners. I would understand that she helped herself through the gate if no one was outside and she wanted to knock on the door or ring the doorbell with her unleashed dog carried or left outside otherwise next to her on leash. Conversing over a fence and/or gate that's low enough for them to have seen you from the otherside of it to begin with, isn't the same as shouting across the street. When the resident of the house is right there, it's up to him/her to open the gate to welcome you onto his/her home or to offer for you to let yourself in.
Again, I'd be wary of her returning, but not so much for your dog, that might have been a disguise for her true interest in investigating your household for future burglaries... That's the kind of world we live in now, sad as it is.