Been there, done that.

Dear Jo;
I have a daughter who became anorexic in her late teens so I know from whence I speak. You need to talk to the childs parents and get her into some counseling right away, before she develops some real health problems.
My daughter was quite heavy at the time her problem started and within no time at all she was nothing but skin and bones. She ate very little and vomited a lot of what she did eat. She would sometimes binge and then throw up.
We originally encouraged her dieting, because she did need to lose some weight. But by the time we realized the magnitude of the problem it had gotten totally out of hand. Her monthly periods stopped, because of no body fat and her teeth were a mess from all the gastric acid from the vomiting.
I would hear her exercising in her room at night, one night I opened her door and she stood looking into the mirror and said "Mom, I'm so fat". Honest to God Jo, she looked like some of those poor starving children you see on tv from third world countries.
We convinced her finally to go to the hospital and get help. She eventually did get her period back and she married and had two beautiful children. BUT,she still has this mindset about exercise and dieting and being thin.
It seems to be happening with younger and younger girls, especially if they are a little plump and the peers tease them about it. I don't mean to scare you Jo, it could just be that she doesn't like something and doesn't want to hurt your feelings by saying she doesn't like what you served. However that is not the impression I get from what you said.
Does she live close enough to you that you can keep on eye on how she's doing?
Perhaps her parents should talk to her teacher so they can kind of keep track of how she does with eating at school.
I will pray that she can be turned around before she becomes really anorexic, it is not only an eating disorder it becomes a whole way of life.
My daughter is compulsive/obsessive about almost every aspect of her life, I only wish we had known then what we know now, and that we had seen it for what it was before it totally consumed her life.
Jo, if you have any more questions please feel free to ask.