The browned starch that forms the webbing/wings is absolutely the worst part about gyoza, or any pan-fried dumpling. I fry mine without it even though that makes the dumplings much harder to lift -- but then I'm not cooking for a restaurant, which is why that technique exists in the first place. The novelty of eating literally fried flour/starch wears off fast.
In any case, most places that sell gyoza use wayyyy too much oil.