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 polite way to settle any friction between individuals. It will not prevent the muted parent from posting to groups or classes etc.
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.