As well as the sensible action that is 'inaction' in such cases I would not only report it, but publicise it as much as possible. Definitely wouldn't spit and rub!

One thing with chalk is that it's very fine and deposits itself in the surface pores of the stone. Removing it often needs to be a damaging process. Charcoal ain't so bad because it disolves in water. I still wouldn't try to remove it though.