Not that the US has a long history of caring a great deal about jurisdiction, but the US ratified the Outer Space Treaty which denies specific jurisdiction over

Not that the US has a long history of caring a great deal about jurisdiction, but the US ratified the Outer Space Treaty which denies specific jurisdiction over parts of the moon to countries on earth. They can likely make laws concerning the LM landing stages they left up there---which probably remain US property---but the footprints would be considered either for the benefit of all mankind or possibly vandalism that the US may be required to clean up by other signatories.