Dogs mostly scratch on the door to be let in or out. Some will whine or circle before resorting to scratching, but some do not. Some only go to scratching when desperate, while others will go directly to scratching a hole into your door. Dogs also scratch if you leave the house due to wanting to be included with the rest of their pack. Now that we know why a dog might be scratching, we can stop the destruction of your doors.
If your dog is scratching because he/she wants outside, stand next to the door. Wait until your dog gives you a full 30 seconds of no scratching. Once your dog has done this, immediately give them a treat, praise them, and let them out. Now reverse it.
If your dog is outside, scratching to come in, wait for the 30 seconds of no scratching again. As long as your dog is scratching, ignore them. Once you hear the 30 seconds of scratch free sound, let your dog in, give them a treat, and praise them. Your dog will learn to associate being separated from you, and not getting what they want, with scratching. They will associate treats, praise, and getting to be where they want, with not scratching.
If your dog is scratching because they miss you, or because they want to go with you, then the same principle can be used, but with some other treatments put into play as well. For instance, try very hard to make a constant routine for your dog. The more of a routine you have, the better your dog will do. If your dog is scratching, you may consider crate training. If you do not want to put your dog in a crate, then do the above, but for longer periods of time as you go. Put your dog in a room. When they stop scratching for 30 seconds, give them a treat in praise. Now do this again, but this time a full minute. Keep going until your dog has learned that as long as it doesn’t scratch, it gets a treat. This can be tedious work, but it is very worth it if you don’t care to have your doors scratched!