This is the clip in which Oswald goes up to Bookhout in the hall and says something to him. I listened to it again, and what it sounds like to me now, as I listen to it again, is, "What have you got against Broby?"
Listen to it yourself a few times and see what you think. There is nothing intelligible I can make out of Broby. But, here's what we know from it. We know that these two, Oswald and this short guy, were in the midst of a conversation, that this was a follow-up to it, a continuation of it. And, I think we should assume it was just between the two of them. I think we should assume it was not directly related to the case. They were heading into Fritz' office for the 6:30 pm interrogation on Saturday. You can't tell me that Oswald was starting it early out in the hallway. But, think about the expression, "What have you got against...?" Isn't it usually a person? It's most likely a person. So, was this a person they both knew? Hear me out:
What if Oswald did the sensible thing for him to do in this situation, which was to start dropping names of people he knew in the intelligence community? Of course, there is no record of that, but that's not surprising. They wouldn't admit to it. So, what if he dropped a name. "I know so-and-so. He'll tell you that I couldn't have done this." So, what if Oswald dropped a name, and Bookhout responded with a disparaging remark about the man he named. And it would have had to be something vague, such as, "I wouldn't cite him if I were you. He does not have a good reputation in the intelligence community." Oswald lets it go at the time, but then later, in the hallway, he asks Bookhout, "What have you got against so-and-so?" And notice that Bookhout doesn't answer. And if I'm right, it's obvious why he didn't answer.
Listen to it yourself with that picture in mind. Maybe something will occur to you. I can be reached at firstname.lastname@example.org.