I don't see where the confusion is. Mikage is just walking into the middle of a conversation between the two, and it's a conversation that Utena and Anthy have had several times, mostly near the beginning of the series. (Episode 2, most prominently, of course.) Admittedly, that does make you wonder why Utena even bothers to bring it up anymore, but eh, she's stubborn. She makes a similar comment in episode 23 also, I think.

Of course Utena hadn't discovered who End of the World was - if she had, he wouldn't be "some mysterious guy," would he?

Oh, I see what you're saying. Yeah, it looks like at some point, Utena picked up the existence of Ends of the World. No, I don't think we ever see anyone sit her down and explain it to her, but she has heard people talking about it - Saionji shouts about it in the area in episode 9, and more importantly, Touga mentions End of the World quite directly when he invests Nanami with a seal in episode 10.

satyreyes wrote:

I was always kind of under the impression that Utena wasn't really listening when people talked about duel infrastructure. 

It is just like her to call him "some dude" instead of "End of the World," though. Who can be bothered to remember some weird pretentious name like that?

(Though actually, it looks like she's not necessarily talking about a singular male person. In Japanese she says "yatsura," or 正体不明のやつら to be precise, which is a plural. That makes sense, in that everyone seems to kind of assume that End of the World is an organization of some kind.)

Wow, that is a big plot hole! I don't know how I missed it. I thought Utena just assumed Anthy was only a prisoner of the Student Council.