First of all, don’t necessarily believe everything you read, certainly not before checking it out. There was once a report of people throwing dirty diapers at the Women at the Wall. Pray tell, where did they get dirty diapers at the Kosel? It later turned out to be false.
But assuming that this story is true, the answer to your question, unfortunately, is that they do not hope to accomplish anything at all. These are people who have a very long history with the establishment in EY, and they are not forgetting it. It is warping their worldview. They are angry and expressing it in what is obviously a highly negative and destructive fashion.
Will they be punished? Go find them first.
How can they be taught to stop doing things like that? Probably, they can’t. Realize that these people are not the ones sitting in the beis midrash learning with hasmadah, or who have regular jobs.
Who can stop them best? No one. The Eidah HaChareidis condemns these things on a regular basis and it doesn’t help. The only thing that might stop them is if the press – chareidi and otherwise – would begin to totally ignore them and act as if they don’t exist. But since the secular press LOVES these stories, I wouldn’t bet on that happening too soon.
Probably all we can do is make clear that they do not speak for or represent the mainstream chareidi community, however defined. Truth to tell, they don’t even represent Yerushalmim. They represent themselves.