I am a little confused about Jeanette. Either Billy is calling this guy, the guard, by a lady name to zing him, or there’s another female guard, Jeanette, who Billy is addressing.
Otherwise your story is streamline and just the kind of thing I was hoping to read.
I’d get rid of the first ‘up’ in the second line. The repetition threw me off a little.
I agree that this is a brilliant opener. It’s an interesting situation that creates a lot of questions. Love the literal take on the challenge. Very clever.