Probably something like <OnCanBeBriefed>, where we can evaluate if the mission can still be accepted. Even something like (msnFireEvent missionObj 'OnCanBeBriefed) would work, but we'd have to handle the case where the mission cannot be briefed and show some language for that (or destroy the mission and exit the screen).
The event could also be used to re-set mission data to make it possible again, so we should be able to pass whether that was successful from the event to the screen; we don't have to destroy/fail the mission all the time in this case.
In API 36 (1.8 Alpha 1) we added the <OnCanBrief> event, which is triggered just before showing a briefing for a missions (before the mission has been accepted). The event can return Nil to indicate that briefing should continue as normal, or it may return a string, to indicate that briefing should be canceled (the string is displayed to the user).
The event is allowed to change mission state or even destroy the mission (with msnDestroy) as appropriate.