I agree with most of the posters here, no need to correct people every time. If it's someone you are likely to see again (a nanny or mother at the park near the house, preschool, etc.) then yeah I would but just in passing, no not needed.

If you're with MB then just simply say "oh, I'm the nanny" or if MB is standing near by say "I'm the nanny, she is their mom". I can see a MB feeling weird about being thought of as the grandma or something so I'd definitely mention it if MB hears.