There is no way to retrieve the swallowed member for the duration of the battle, and that character will not gain EXP or AP upon the Zuu's defeat. Eating it gives the Blue Magic spell White Wind, which can be useful at that time in the game considering Dagger, the party's main healer, is not usable.
[view·edit·purge]Zu means "fire" in the Sumerian language. Anzû, before misread as Zû, is a lesser divinity or monster in several Mesopotamian religions. He was conceived by the pure waters of the Apsu and the wide Earth, or as son of Siris. Anzû was seen as a massive bird who can breathe fire and water, although Anzû is alternately seen as a lion-headed eagle (like a reverse griffin).