Don't we all?
IMHO this is merely a case where the attention of the people that hired us was never on a personal level. They simply see us as a service instead of as a person. This might hurt a bit in the context of babysitting because we didn't just come to deliver something and be on our way. We came to care their precious child(ren). This should be something people remember, right? Apparently, not. Apparently to some people, the person who took care of their children was simply a service, not a person.
Nevertheless, if I were in your shoes, I'd probably feel the same thing. I would play along with the new introductions, but probably with small signals of "been here, done that, give me a break." In the end, I'd probably won't think too much of it. I mean, if we're just a transaction to them, then they are also just a transaction to us, right. Why bother connecting to the disconnected?