Brush the damaged area of the muntins with a wire brush in the same direction as the wood grain. Remove all of the loose, rotted wood and debris from the muntins.
Chip out all of the rotted wood in the muntins with the tip of a putty knife. Brush the cleaned-out rotted spots with the wire brush.
Brush an even coat of epoxy primer onto the damaged areas of the muntins with a natural-bristle brush. Allow the primer to dry for at least four hours.
Fill the damaged areas of the muntins with epoxy filler, using the blade of a putty knife to pack it into the wood. Smooth the filler over the damaged areas so that it is just raised above the wood surface. Allow the filler to dry for 24 hours.
Sand the repaired areas of the muntins with a fine-grit sanding pad. Be sure to sand the dried epoxy filler in the same direction as the wood grain. Continue sanding until the filler is flush with the surface of the wood.
Brush on a coat of primer and a top coat of paint using a paintbrush. Allow the primer to dry at least four hours before applying a top coat of exterior paint.