A thank you note was a letter written to express appreciation or gratitude to someone for an action or gift.
In 2370, after a successful maneuver, Jadzia Dax asked Kira Nerys to remind her to send a thank you note to the assembly teams that put together the USS Orinoco. (DS9: "Paradise")
In 2373, Ishka told how she and Grand Nagus Zek began corresponding after she sent him some pointers at the Global Tongo Championship, which he then employed successfully. He then sent her "a very nice thank you note". (DS9: "Ferengi Love Songs")
In 2377, Captain Kathryn Janeway noted that she would like to send Lieutenant Reginald Barclay a little thank you note for all his hard work. (VOY: "Inside Man")