Caller ID says "Hearing Service".  They leave no message.

I call back during business hours (using *67 to block my number).  I hear the following, "Thank you for calling Hearing Health USA.  We're not available to take your call.  Please, leave your name and number and we will get back to you.  Thank you."

I did a quick check with google.  There is a company with this name.  Looks like they buy up audiologist's offices and sell hearing aids.  I personally would recommend going to your doctor first if you need a hearing aid.  They can steer you toward a reputable product that suits your needs/budget.

I am on the federal do-not-call list, so cold calling me seems to be a violation of the law.

I suppose it is also possible that a medical scammer is spoofing their number to sell crappy products and bill medicare for expensive ones (think back braces, et al).  This would only work if you picked up the call; calling back would get the real company.  The fact that the caller ID does not say "Hearing Health" makes me think this is a real possibility.