Whisk lemon zest and juice, garlic, oil, black pepper, salt, and oregano in a large bowl to combine.
Add wings and toss to coat. Cover and chill at least 2 hours and up to 12 hours.
Place racks in upper and lower thirds of oven; preheat to 375°.
Line 2 large rimmed baking sheets with foil; set a wire rack in each one if you have them.
Remove wings from marinade; arrange on baking sheets.
Bake wings, rotating baking sheets front to back and top to bottom halfway through, until deeply browned and crisp, about 1 hour.
Whisk oil, lemon juice, garlic, cayenne, and black pepper in a small bowl; season dressing with salt.
To serve, stir parsley into dressing. Arrange wings on a platter, drizzle dressing over, and scatter feta on top.
