The Two-sided note is a mundane item found by Nino in the forest where he saved Five, on the right hand path.
The Two-sided note has 2 sides with 2 different people speaking on it. On one side an aqua-blue note says, "Shit's mine so get lost ya fuckin kleptomaniac sucka - k". This is referred to as the unpleasant note. While the other has bright red text saying "Sorry about that - T." Presumably referring to k. This is referred to as the apologetic note. k is Kaji, due to the exact match between the color on the note and his text color when he's speaking, the fact that Kaji starts with K, and the fact that Nino notes in the Icicle Bay Gateway panel "But for some reason, the writer's tone sounds familiar..." This part of the inventory description is added after Nino meets Kaji. Kaji confirms this when inquired about it after they make peace as well, The Maids of Red's Inn didn't steal Nino's note due to it being useless.
Later on, Nino returns the note to Kaji, which he is grateful for, saying the note brings back good memories. However, when returning the note, the formerly red half of the note changes to a golden-yellow color, which Nino inquires about, but ignores later on. The note is implied to be somehow tampered with, as in the tumblr Q&A, Nights confirms that the note was formerly red, and Nino was now seeing it as golden-yellow, affirming that the note's change of color wasn't a retcon.
The note gave Nino +1 stupidity point by him kicking the box from where the note came in frustration. This caused Five to be intrigued by Nino's behavior, granting her +1 curiosity point.