From the Super Mario Wiki, the Mario encyclopedia
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Comet Pieces are pieces of the Sticker Comet which serve as the level's goal in Paper Mario: Sticker Star, allowing progress in the world map. They can be found flashing between different colours, and collecting it will show a "Goal" screen where Mario can collect bonus coins. Most non-boss levels have at least one, with the exception of Outlook Point and Shaved-Ice Cave. If 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 in containing three Comet Pieces.
In World 1-3 Water's Edge Way after Kamek's defeat, he pulls the Comet Piece from its place via Paperization, transforming it into a scrap and tossing it away to the waterfall. It must be retrieved and Paperized back into place before being collected.