how to unpublish a listing

On our site we have doctors and locations as “listings”. The doctors have “categories” they are associated with. On occasion we have doctors that “retire” only to come out of retirement a year later. So we want to be able to “unpublish” them but cannot.

Here is a page where we want to remove the doctor from https://www.rockymountaincancercenters.com/medical-oncology-hematology/

We can’t even REMOVE the category they are associated with to take them off this page.

How can we accomplish what we need?

Thanks!