From the Super Mario Wiki, the Mario encyclopedia
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Comet Pieces are pieces of the Sticker Comet. They serve as the level's goal in Paper Mario: Sticker Star. Every level has at least one, except all world-boss stages, Outlook Point and Shaved-Ice Cave (Decalburg and Surfshine Harbor as well if they are considered levels).
Sometimes, there is more than one Comet Piece in a level. The second piece usually serves as the level's secret exit. Wiggler's Tree House is unique, as it holds three comet pieces.
They continually flash between the colors, blue, green, red, and yellow, however, they stay the same color as they were when hit by Mario, thus completing the level.
In World 1-3, Water's Edge Way, after Kamek's defeat, he pulls the Comet Piece from its place via Paperize and tosses it away to the waterfall. It must be retrieved and collected as a scrap. It can finally be collected after re-pasting it in.