Training a dog not to scratch doors

Get an e-collar. This way, you can remotely correct him when he does the behavior. If he's already trained to the invisible fence, this should be a quick and easy fix. You can set the e-collar to a beep, vibrate or mild shock, same as your invisible fence. I would bet in 3 days, you will not have anymore door scratching.

I SO AGREE with you...I was told to help stop digging around the fence, put chicken wire around your fence because dogs hate how it feels. I am thinking to cut a piece and staple it to my door. I have already replaced a door my dog scratched up costing me $300. We have moved and she is back doing the same thing. Crossing fingers and hoping this works. It has worked around my fence.

I agree with you that training a dog to behave is showing love, not lack of responsible ownership. Each situation is different.
We have a fenced in yard facing the canal (no cars), several large shaded areas, and a pool with a large sun shelf they love to wade in. My 2 dogs either whine or yip to come in. The doors are hurricane-strength heavy glass with a sun-protectant coating - very expensive.
The problem is a friend's 6 year old lab mix I dog-sit who is used to scratching to get in. I can't stand and watch him ruin the coating while I wait for him NOT to scratch to let him in. I can't put a cover over the glass or out anything outside to keep him from getting close. I'm curious about the "scat mat"; is it expensive? We have 3 doors! I may resort to slapping a flip flop on the door when he scratches. Any other ideas are welcome (not sitting the dog is not an option).