Sand the worn, chipped area of the luan door lightly with a fine-grit sanding block in the same direction as the wood grain.
Spread an even coat of high performance wood filler over the worn, chipped area of the door using a putty knife. Leave the filler slightly raised over the worn, chipped area and feather it out past the area so that it gradually blends with the surface of the door.
Allow the filler to dry for at least four hours and sand it with a progression of medium to fine-grit sanding blocks until the repair is completely smooth. Sand in the same direction as the wood grain. Wipe off the dust left from sanding with a tack cloth.
Apply a light coat of a matching wood finish touch-up with a natural bristle brush. Allow the coat to dry for 4 hours and apply a second coat.