I would certainly let the parent know how they are going about feeding her. The parent has a right to know that they are practically torturing this child and that are probably creating food issues for this poor child in the future.
My own baby, though not tongue tied, started not liking baby food at around 8 months. I could not get more than one baby food jar in her a day. She went from the 60% to the 30% in weight. So I started giving her more table food. She was much happier and started gaining weight again. There are still days where she does not consume a lot of food but since overall she is eating more, I am not so worried.
A daycare should mimick what is happening at home. This child is not a good fit if the teacher and director have such strong opposing opinions how how to raise this child from the parents.