I know how your mum feels coz I find it hard to tell people "dont't touch my kid" but really, she HAS to be more firm. Just tell her to be firm and say no!!!
Hygiene aside, not that I'm paranoid but you'll never know what these people can do. Say carry but they can easily run off with your baby once your baby is in their arms!
My hubby will actually scold people - he has been told that it's just simply okay to tell people off here in Singapore. :/
In my case, I just go "Excuse me, do you mind?" and they usually back off. Either that or I look super pissed and they'll just back away and admire from far. :P