During an ATE during Disc 1 Vivi will receive an item called a Kupo Nut. Later as you're going through Gizamaluke Grotto you'll encounter some newlywed moogles and your Kupo Nut saves one of them. The male moogle you saved says that if you find any more nuts that you should bring them to him. Later, as you're delivering letters for Mognet some moogles will give you Kupo Nuts.

However, you can only have one Kupo Nut in your inventory at a time so you'll need to return to Gizamaluke's Grotto as many times as you can to give the moogles your nuts. For each nut you bring they'll give you an item. The item you're looking for is an Aloha T-shirt. During the Chocograph sidequest you'll encounter a treasure trove that includes 8 items of a Hawaiian set of gear, enough for each of your party members, but there is one missing Aloha T-shirt.

You'll definitely want to remember to deliver your Kupo Nuts when you decide to pursue the Mognet Central Sidequest because each moogle you deliver a letter to will give you a Kupo Nut. Your rewards for pursuing this sidequest are the items and seeing the moogle offspring run around the little room in Gizamaluke's Grotto.