Mary Lou, exactly what sort of insulation are you talking about here? Do you mean the weather stripping? Can you post us a couple photos of the damaged areas?
Most doors have removable insulation strips. They are usually round with little tabs that push into a grove within the door edge or along the frame.
If you know what kind of door you have (make or brand) simply go to any lumber yard or door seller with store that sells that brand and they can order new gaskets for you.
My dog does this all the time. The rubber is always tearing as he tries to scratch to get in. Do not tell him, but hes getting a doggie door for Christmas.
The dog or insulation? One of the joys of pet ownership (I know, I'm being a smart a _ _) But it is kind of funny:) I crack myself up somtimes