Qi Fruit is used in the spool of Sewing Machine with Cloth in the feed to create a Qi Mask. It can be placed in the blue dye pot at Emily's and Haley's house for use in dyeing.
Finishing the Qi's Crop quest does not remove Qi Fruit in Pierre's General Store stock. Extra Qi Fruit can be sold to the General Store before completing the quest and bought back the next day for 1g each. This makes future Qi's Crop quests significantly easier. It is possible that Villagers may purchase some of the Qi fruit, resulting in fewer fruit to buy back.