I have a new baby who just started and I noticed at the interview that he was pulling his Mom's hair and poking his finger in her mouth and I had to explain that in a daycare that is unacceptable. If he pokes his finger in another child's mouth he will get bitten and it will be the other child's fault and if he pulls hair the other children won't like him.
Explain these things to the parent, that we have to teach all the children respect and empathy and kindness toward one another and we don't want any injuries or sadness, just happiness. In my case, the child is 14 months old and the parents never thought about the behaviour before as being unacceptable, they didn't have any reason to put a stop to it before in their eyes.
I wouldn't be mortified, it's a natural thing and children all push their boundaries to see what they can away with until we teach them what is allowable. I'm sure the parents will be fine if you explain it the way I explained it to my dcparents.