Quest Giver: Moggie
Reward: 1x Moogle Membership Card
The Mysterious Moogle Merchant becomes available in Chapter 8 after completing the ‘Escort the Children’ main objective. This furry child is a Moogle superfan located at the Children’s Secret Hideout who’s willing to trade special items for Moogle Medals. All you need to do to complete this quest is to buy the membership card, which you should have medals for from all that crate smashing you’ve hopefully been doing.
Also, while you’re here, you should purchase the ‘Graveyard Key’ for 1 Moogle Medal (you’ll need it for a later sidequest, “Paying Respects”) and the Gold Saucer track because why not?