Take the Rhinostery Canteen he gives you to Giddeus to the spring at (K-12) or (E-12) and trade to it for a Canteen of Giddeus Water. (Note that if you have access to Domenic's warp service in Lower Jeuno, you can warp to Balga's Dais which will put you very close to one of the springs when you zone out to Giddeus. Alternatively, if you've already visited the Giddeus Homepoint, you can simply warp there yourself from any Homepoint at a cheaper rate than what Domenic offers.)
The Rhinostery Canteen is a usable item, and you can 'use' it on the spring. As such, it will appear at the beginning of the item list, not after the equipment items.
This quest cannot be repeated if you have activated the quest Curses, Foiled A-Golem!?. Talking to Leepe-Hoppe on the roof may activate Tuning In, which may also make this quest non-repeatable (or at least until Tuning In is finished).