If you want to delete a classification of one of your classes on a dedicated level you have multiple options here. This Brainwave will briefly introduce you to the most basic one, deleting a classification from within the Class Hierarchy window.

If you right-click on the class you want to delete (it will delete the classification but not the class itself), choose "Delete Classification". What this will do is, delete the classification of that class on all Image Object Levels that are currently displayed in the View Settings. If multiple Image Object Levels are currently displayed all displayed levels will be affected.

Enjoy deleting classifications :D.