From the Super Mario Wiki
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The Mansion Door is a scrap found in Paper Mario: Sticker Star. Mario is required to retrieve it in The Enigmansion by traveling to the library to the right of the mansion's front entrance, defeating all of the Boos in the area, and jumping up to the bookcases to obtain it.
Mario must then travel up the flight of stairs by the front entrance, then remove the Steward's Portrait and place the Mansion Door into the resulting blank area, allowing him to access the second floor of the mansion.