Deleting objects may be a bit confusing at first: If you have NOT selected any objects then it may look as if the delete button is not working as nothing is getting deleted. See a simple tip at the end of this topic
The reason is due to the presence of helpers on the current object. Usually TAD works on either the current object or on the selected set of objects. However, in case of deletion, TAD will work ONLY on the selected set of objects! The reason is simple: TAD is quite religious about ensuring that the helpers are always located on some object or the other.
If the object where the helpers are sitting is itself to be deleted, then logically speaking, TAD get confused: It does not know where the helpers should go next! Hence it will not permit the deletion of the current object
If you want TAD to delete that object too i.e. delete the object where the helpers are placed, then first shift the helpers to another object (An easy way: Click on another object name in the list of objects displayed in the top-left of the screen) and then select the earlier object (the one which the helpers used to sit on) and add that also into the current selection list. And then press Delete.
There is an easier way to delete ONE object at a time (If that is what you prefer) Just right click on the object name in the list of object names displayed (next to the class tree) and then select the delete sub-menu item! If it is grayed out, then it means that object is the current object and cannot be deleted.
Press F1 inside the application to read context-sensitive help directly in the application itself