I like bringing this stuff up face to face as it gives them less time to think of a response!
I would have said “sally keeps talking about her teachers at daycare, is she in daycare?” and see what mom says. Then term on the spot!
I actually found out that a family was leaving because the kid told me they went to a new school and she was going to be starting a new school soon. It is hilarious that parents think kids won’t tell us