Yes, I believe it is a common American thing to call a Polish grandmother Babci.
Probably because after time, the descendents take the basic root word and add the kind of ending that makes sense to American ears. The way we make English words informal and cute. Like Bobby instead of Bob. Puppy instead of dog.
But what is forgotten is that kind of ending does not do the same thing in Polish. Michal is Michalek. Kot is kotek.
So it is an adaptation and corruption. But that is what I called mine, too. I never knew it would sound strange to someone from Poland. And then I found out when my Polish bf laughed at me calling myself Babci.