I'd like to stop here for a moment, because... has it?
I mean, at this moment in fiction: what triggers the duel, exactly? What are the stakes? At this point Alex wants nothing from Mhairi and accepted there's no removing her as Director in the forseeable future. Likewise, a Pledge has proven he's not a Loyalist, he's given up on being Groundskeeper and has not insulted Mhairi in any way (in fact, he was trying to do something completely opposite).
Sure, like you said: a Duel doesn't require a reason. But there's nothing for Alex to give away unless it's to the death or banishment is at stake. Which is kind of extreme if the reason is 'I don't like your hair'.
I'm not disputing the possibility of a Hedge Duel (Alex'd concede anyway because of the immensely uneven odds), I'm arguing it's stoking the fires of an IC conflict that has already ended.