that has been chewed. How many steps have been chewed? Is there a place where you can take some carpet from to do some patching, like a closet or something?
Is this a plush carpet? Plushes are easier to patch than others.
I am thinking about cutting a nice square area out of the closet and the same size from the step. Then get carpet thread and needle and sew the carpet to each other from the back side. Then re attach. But, you do want to make sure the runners are safe, especially with lookers going up and down the steps. Could become a liability issue.