I think a lot of people would be very offended by her picture, it seems just.. really needless. Being spiteful about a group like that is a strange thing to want to do, it seems a better way to spend time would be to make a picture about something that hurts people/the world, rather than an organisation that seeks to help people who are suffering. I guess the girl who posted the picture and emailed you must have her own issues and just doesn't 'get' mental health issues, perhaps she has issues herself and hasn't found a way to deal with that, who knows. Even when people don't get it though, I wonder what motivation they could have to mock or make cruel comments that will affect other people.

I'm sorry you've been upset by her email, I think you were brave to stick up for the organisation though and try to get her to see how cruel her actions and words against it was.