I think this order was given when the FBI realized LHO had been working with DeBrueys in New Orleans that summer.
Based on things that he learned later, Hosty makes a reasonable case that he believes that it had to do with the top FBI officials trying to keep a lid on the Mexico City aspects of the case. Here’s another excerpt from “Assignment Oswald”:
“Ken, how did Shanklin find out about the Oswald note so fast?” I asked. Howe explained that after Oswald was arrested and his picture was shown on all the TV stations, Fenner recognized him as the guy who had brought the note in ten days ago. She reminded Clark about the note, but Clark couldn’t recall it. Then Fenner told Howe and Shanklin.
In 1979 I learned from Clark that he had received a call the day of the assassination from Bill Sullivan, one of Hoover’s other top assistants, who told him to make sure I did not see the communique from the D.C. field office about Oswald writing to the Soviet Embassy in Washington. Clark then told Howe to keep the communique — which had just arrived the day of the assassination — and any others concerning Mexico City from me. Howe knew I had already seen the communique that afternoon, but he decided to remove it and other related memos from my file drawer so I couldn’t see it again. Going through my file drawer, Howe came across the Oswald note and took it to Shanklin. Howe said Shanklin instantly became livid. How was this going to appear to the public, and especially to Hoover, he wanted to know. I told Howe I still didn’t think the note was that big a deal, and what we had to do was put it in context. Howe shrugged. I went back to my desk and began reviewing my Oswald file again.