The sentence that uses a verb that agrees with its pronoun subject is Choice A. Neither of the restaurants delivers to this neighborhood.
The verb "delivers" is in singular form. This is because "Neither of the restaurants" is in the singular form. It means "not one of the restaurants."
Choice B. should be. Is everything in the basket?
Choice C. should be. Nobody among them is complaining to us.
Choice D. should be. Something in the soup tastes unpleasant.