You'll have to have spoken to Peatrice a number of times throughout the quest at the Bazaar. After speaking to her a number of times between dungeons, she eventually warms up to you quite a bit and starts to call you darling. At this point, enter Peatrice's house at nighttime, located just east of the Bazaar.
Speak to Peatrice's father Peater ,the man who runs the mini-game on Bamboo Island, and he is worried that his daughter has an unwanted admirer. Peater asks you to keep an eye out for this certain somebody. Kind of hard if the certain somebody he is talking about is actually... you? Anyway, use the bed in the house to return to daytime.
Go back to the Bazaar and you'll find a speech bubble over Peatrice's head. Speak to her and she mentions that she wants you to visit her house tonight. Sure thing! Return to a bed in Skyloft to make it nighttime.
Return to Peatrice's house at nighttime and speak to her. She will ask you how you feel about her and you have a choice on how to respond. If you speak to her and say that you like her, she'll warm up to you and you'll get five gratitude crystals!
The alternative is to say that Peatrice is just the girl at the item check and nothing more. While you were break her heart, it will lead to the same five gratitude crystals. Sleep in the bed nearby to the next night and then speak to her father Peater. He is pleased that his daughter has finally given her admirer the boot. As a reward for helping him out, he'll give you five gratitude crystals!
NOTE: It's possible you can only complete this sidequest after the 2nd or 3rd dungeon, but most sites don't mention when it becomes available.
Answer courtesy of Zelda Dungeon .net