The question wasn't tailored so narrowly. You write: "The intriguing question is whether Gheesling and Anderson took Oswald off the security watch list based solely on the report about Oswald's cooperation with the FBI, or whether they had also been tipped off that a molehunt was about to begin with Oswald's file." Golitsyn told the FBI, including Hoover, either directly or indirectly, that there was a Soviet agent in the Washington FBI office.  You ask why was Oswald taken off the watch li