Sometimes the best answer is make them go through the process and find out that department heads will not support them.
Good point. Given the few replies and large number of views for this thread, that may be the only thing to do.
I often warn students that challenges or grievances will not prevail unless they can demonstrate that their complaint is based on demonstrable unfairness (that is, they were treated differently than other students) or unprofessionalism on the part of the professor.
That usually keeps me from hearing from the students with groundless complaints. Just had one last week. A student wanted to grieve against one of my faculty members because the student really, really, really needed a C in a class from last semester and was only 32 points away from one (on a 200 point scale). I explained the grounds for a grade challenge (which she couldn't meet, clearly) and she swallowed and decided to take the course again.