There is a "Admin can edit/delete ad" parameter available in DJ-Classifieds general settings.

It allows the administrator who is assigned to "Super User" after login on the front page to edit and delete adverts like advert owner. 

To enable this buttons open the DJ-Classifieds component and go to options.

This option you'll find in general settings.

Choose "Yes" and click "Save" - "Edit/Delete" buttons will be displayed on the advert details page.