Hi Bill.  I wasn't actually familiar with the "muted" property for an assignment, but when I found it in the Assignment definition in the Rest API documentation there's a note that it is Deprecated.  Perhaps because of that the property can't be set/updated via the API call?

I actually don't see the "Mute Assignment" option in Gradebook UI anymore.  Is it still available in your Canvas version?  As far as I'm aware, it was replaced with Grade Posting Policy a little while back.