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.

There are a few options depending on the circumstances, if the dog has scratched the slab and depending on material, you'll need an entirely new slab. You have the option of painting over the scratch, but the odds of that peeling into the future are high. Our doors are steel and fibreglass, fibreglass would require an entirely new door slab to be installed if you wish to rid the problem for good. To surely rid the problem, the dog or puppy should be trained before repair unless you want to experience a fruitness endeavour. 

When dealing with a wooden door, their are a few DIY solutions like sanding, filling sanding again and painting/staining over. 

It looks like the pup teaches classes on how to be a beaver 101. Sanding, filling and matching the colour back would be the best option in this circumstance, or simply an entirely new replacement. 

Cut the screw if the other methods fail.

Hello I am Ken From KP Carpentry. Can you tell me more about your built in project? Do you have a design in mind? How big is the area? Can you take a few pictures of where you would like it to go?

The leak and mold are time sensitive. Mold can be hazardous to your health. Dealing with mold properly means removing the sheetock and insulation once the leak is fixed. Don't let anyone tell you they can seal it in place and paint ove it. It must be removed. The foundation work can get vey expensive if you wait too long so don't put that off too long.

Hope this helps.

I agree with what Yuri said and would like to add that it is imporatant to have it removed properly so as not to cross contaminate. Mold spores are microscopic in size and easily dispersed if not handled correctly.

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.

It can definitely be repaired, it would need extensive spackling, most likely with 2 part Bondo, then sended primed and painted.

this is something that should not take more than 6-8 hours in total, obviously it does require some skill.

Try securing the anchors with ViseGrip pliers, but be sure to only secure the anchor, not touch the screw.

There is a bee spray you can mix in a pump up and reach the higher carpenter bee holes. This worked for me.

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.  

That is Oriented Strand Board (OSB), typically used for sheathing.  Looks like it has been used exposed to weather, which is not its intended use.  There is no reasonable repair for that, other than replacement... with materials suitable for whatever the application might be.  Call a professional contractor.

I have seen a lot of great DIY carpenter bee traps that fill up with bees. I have friends that say the traps keep them out of the house. 

https://www.pinterest.com/explore/carpenter-bee-trap/