Items bought in the souvenir shop and all theflora/ fauna you caught or collected in the island should be placed inside the box beside Leilani’s counter. You can’t take home rental items. Since you only have a limited number of items to take home, you should consider bringing only the ones worth the most bells.
For your first visit, I suggest taking new species home and donating them to the Museum. Refer to this guide’s fish, bug and Sea Creatures List to know what creatures have the most value.
Leilani
Talk to her to try out different tours or mini-games. These mini-games will earn you medals which you can use to purchase unique stuff from Grams’ souvenir shop. These mini-games can be played alone though some of them may be better off playing with your friends. Higher difficulty / ranked games will earn more medals. After choosing your tour, simply sit in the waiting area to be transported to the tour location.
If you want to go back to your town, you have to talk to her as well.
She’s the old lady that runs the souvenir shop in the island. The items she sells changes every day so it will be worth holding on to those medals you’ve collected in case you don’t like any of the items she’s selling. You can earn medals by completing tours.
She’s the kid that will buy any item from you for a very small amount of bells.