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The picture shows the door is stained wood. The wood is repairable but the door will have to be painted or the repairs will be visible.
Do you know if the estimate from Home Depot was to replace the entire door assembly or just the (door(s)?). If they estimated the cost including removal and replacement of door jambs, threshold, and door trim, then an alternative that could cost less would be to replace the door slabs only and keep the existing jambs and trim.
Its painted; go to hardware store. Buy spackle and sand paper. Sand it down, spacke the scrapes. Sand the spackle. Repeat again, though after this spackle prime the door. Then spackle and prime and paint. You are looking at spackle 3 or more times, priming it more than once and then paitning two coats. Alot of work. But less expensive than a new door.
As with the previous comments, you can use sandpaper to smooth out some of the damage, but be sure to rub the scratches along the grain of the wood. Next, apply mineral spirits (these are solvents made from paint thinner and petroleum) over the sanded area. Spread on wood filler with a Spackle knife to the damaged parts and allow it to dry as per the filler’s directions. After the wood filler has dried, lightly sand the area once again and brush away any dust before priming and painting your door.
While the image shows damage to the inside of your door, your pet may try scratching on the outside of door and its weather stripping in an attempt to be let inside. In order to prevent future damage to that part of your door, you can add a piece of vinyl lattice that matches the color of your doorframe. Cut the lattice to the length of the doorjamb. Place it over your foam weather stripping. Check to see that your door continues to close properly. Use finishing nails every foot to tack the vinyl lattice securely in place. A small amount of spackling will cover up the nail heads. Now the lattice will protect your weather stripping from further damage.
The right type of door for your home can make a huge difference. We install ProVia doors and they offer DuraGuard Series Storm Doors, which are ideal for keeping pets safely inside with their non-removable stainless steel screening.
Best of luck with your dog and your door repair!
I would concur with the above answers. If you are able to fill with wood putty and paint that would prove to be the most cost effective option. If you would like to go further, determine the brand of the door and I'm sure you could find a replacement sash. I am like you, I love my dog like my children, continue to be patient and show your bowser the love he deserves.
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