If you speak regularly with Peatrice, the Item-Check girl, you should notice that she begins to develop feelings for you. After speaking to her enough times, she will start calling you “sweetie” and “darling.” At this point you must find Peater, her father.
Peater can be found on Bamboo Island during the day and inside of Peatrice’s house at night. He tells you that his daughter has an unwanted admirer and asks you to watch out for him.
Return to the Bazaar during the day and talk to Peatrice again. She will ask you to visit her house that night.
When speaking with her at night, you have two options. First, you can respond to each of her questions with statements that suggest that you have feelings for her. When she is finally done questioning you, she will reward you with 5 Gratitude Crystals.
Your other option is to tell Peatrice that she is just the Item-Check girl, breaking her heart. Afterwards, talk to Peater to learn that Peatrice’s unwanted suitor has left her alone and to receive 5 Gratitude Crystals.