Coffee we have 3 children & my DH has never had to 'have words' with an elderly lady - I can't believe the OP's baby is such a massive old lady magnet that was necessary.
I'll make it clear I'll talk to anyone, and a smile and a chat to an awake baby has never bothered me, I talk back, I don't find anything strange with talking to strangers, and regularly do.
But I've "had words" before.
Brought DD out after a massive puking screaming reflux related incident, just gone to sleep, lady pops in the queue behind us in iceland, actually pulled the hood of the pram back to see her better and then proceeded to cheek poke, OH said "excuse me? Sorry but she's not well and we don't want her to wake up" Lady was shirty with us, but christ, she was pulling at the pram!
Took her to the doctors and a lady came up to me while daughter was screaming in the waiting room (just had her jabs and was only in a nappy waiting for doctor) poking her tummy and saying "oh she's hungry" (she wasn't)
And I have had so many people actually poke and touch my daughter and it just bothered me, like it would if anyone I didn't know started getting physical with me lol. Never had children and never been interested in other people's so it genuinely took me back.