There's no need to peel the zucchini and if you have a medium or smaller sized zucchini you don't need to remove the seeds. However, if your zucchini is large, you should remove the seeds. A large zucchini has well formed seeds, that are tougher and toften taste bitter. They will not be pleasant in the zucchini bread, so it's recommended that you scoop them out before adding the flesh to the bread.