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 assumed to be 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 only is added after Nino meets Kaji. The maids of reds inn didn't steal Nino's note due to it being useless.
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.