It is possible to mute a parent if you feel you don't want to receive any more private messages from them. This feature can be a be a non-confrontational way to settle any friction between individuals, but note that the muted individual will not be notified that they are muted. It will not prevent the muted parent from posting to groups or classes etc, and if they are included in a joint message thread you will also see their messages.
The process is very straightforward: search for the parent in your Classlist page and click their name to bring up their profile. At the very bottom of the page there is a 'Mute' button. Click this to mute, and click again to undo at a later date if you wish.