To remove the peeling poly use a stiff nylon scrub brush and a little warm water. You can also lightly sand with a fine sanding sponge. The idea is to remove the loose clear coating and not damage the stain. Do not aggressively sand as this will harm the stain and door surface.
Now wipe down the door with liquid sander, a cleaning solvent. Paso is the best but see what is available in your area. If nothing is available use denatured alcohol.
If everything went well you are now ready to apply a new coat of clear sealer, 2 coats is best. An exterior spar varnish is much better than polyurethane. McCloskey's Man-O-War marine spar is the best.