Note: Class types that are configured on classes or other entities are in use and cannot be deleted (the delete action button will be greyed out in this case). In order to delete a class type in use first check the References tab on the Edit Class Type panel to determine which entities are configured with the class type. Next, proceed to modify those entities to use an alternate class type.
Select the class type on the left under the Classes Panel or use the Filter text box to locate the desired class type
On the left under the Class Types heading click the icon
On the confirmation dialog click Yes to confirm that the selected class type should be deleted