I need a quick cheap way to patch a molding?

Question

My dog dug into the molding around the door. It's about 1/2 in deep and about 4 inches long by one inch wide. I don't know much about home improvement or anything like that but I need a cheap quick easy way to fix it so my apartment complex doesn't charge me for it.

Answer 1

Use a wood filler. The newer plastic type will not shrink as much as the older wood products. Then sand and paint.

Answer 2

I would use a water based wood filler.  Apply it with a putty knife and sand smooth, paint the same color.