Hi 3image.

In this short tutorial I show you a quick way to delete holes in simple situation just like the one you described :

http://take.ms/ig9Lg

These are the main steps :

1) Select one of the hole's faces
2) This is the trick : PERFORM A BOX SELECTION OF THE HOLE USING CTRL+SHIFT AND DRAG
I this way you can select all the hole's faces in one single pass
3) Delete the selected faces
4) Select one of the edges of the model
5) Perform a "Select All" command
6) Delete all the selected edges

In that way all the trimmed surfaces go back to being untrimmed and the hole disappears!

P.S. Just take a look also at this very interesting Chipp Walters's tutorials :
https://www.youtube.com/watch?v=5QCyXglgBzs
Removing Fillets in MoI3D

Best,