All and each grade my daughter was in, from Preschool, the Teachers have ALWAYS, spoken to the ENTIRE class, about behavior and teasing and name calling and what not.
So, if something like this happened, well I would speak to the Teacher. Who of course wanted to know, SO that, they can, talk to the class, about what is mean/nice, appropriate/not appropriate.
Then at home, you can also speak to your girl, about herself. About nose picking and how that is something you do at home, or in private if out of the home. And that, a person can get sick that way. Germs are on hands, if you pick your nose, you can then get sick. Thus, wash hands and keep clean. My Husband for example, will get sick, when he bites his fingernails. And the saying always goes, during cold/Flu season, if you put your hands to your face, you can get sick.
So maybe teach your daughter about this. Basic hygiene and just the facts about it.
My daughter, has a classmate that picks her nose. And well, all the other kids know this. THEY find it... gross.
But they are her friend, and they tell her. Because this girl will pick her nose, then is very 'huggy' with other kids, and they get grossed out. They don't want to get hugged, after she picks her nose.
Who would?
So it is a fact... people see picking your nose, as gross. Who wants boogers, on them? And then the person uses their hands to touch other things.
I would really, since your daughter is already 7... just speak to her about her nose picking habit. Because overall, you said she is a nice kid... so even more so, she should know about how habits like this, can gross out other people. It is done in private.
My son is 5 and a nose picker. But I teach him, that as he gets older, others don't think its cute or funny. It is.... icky.
He understands.