Perhaps you could change the phone number registered with the HMO to a Google voice number, and then block the source of harrassing calls. Or at least let them leave voicemail, which you can cheerfully delete based on text transaction without ever listening.
My 40something wife would love it if our HMO would stop calling and emailing her 6 times a year to get a mammogram. She has explained clearly to her gynecologist her reasoning, that she is absolutely not going to get a mammogram before age 50, but the annoying calls do not stop. (We shut off our ringer, and use a Google voice number for people we want to her from.)
Much as I sympathize, breast cancer survivor groups have many characteristics of a religious cult. They have paid a high emotional and physical price for entry, and as a result they are so bought in to the idea that the treatment-torture saved their lives that they have only a limited ability to think rationally about health issues anymore.