Need to fill cat scratches in wood!?!

So my cat decided to use the corner of a doorway to sharpen her claws and I am moving in a month. I need to know what would work best to fill in these scratch marks. Then i will sand it and paint it. The door has like a wood boarder around it and that is what is clawed up and it has detailed grooves in it.. someone pls help i want my damage deposit back..