Another solution is that the OP has alluded to working on computer and listening to pass offs during their lunch time which shows any administrator that they are already giving up their duty-free lunch to work.
My suggestion is to respectfully discuss the situation with the HBD and talk through the situation as professionals. Also, stop doing work during their duty-free lunch and find a way to finish the computer work and listen to pass-offs at a different time. My high school band director gave this piece of advice when I started teaching: "Don't do anything for free. The moment you do is the moment the administration will expect you to do more than you are contracted for."