I have a solution that works for me very well.  I too live in a rental
place and I just got brand new carpeting last fall.
 
On the floor on the side they do the most digging, usually the door knob
side, I layed down tape...It is the CLEAR packing tape, I made a 4inch by 8
inch patch two layers thick.  What is nice is that it is clear so It is not
to noticeable and the fuzz brats dont get the same enjoyment out of digging
at it..IT REALLY WORKS!!  and you can still have that Martha Stewart home!
(G)
 
Try it...let me know how it works.
 
June and the NON carpet diggers
[Posted in FML issue 2676]