yes, they've been discussed.
Apparently there was a listening device planted at the meeting or one of the conspirators was nearby close enough to hear.
The person sitting is the CinC's 'aide de camp' asian officer. She sits there after introducing the CinC.
why she is there later is not explained. She is there thru part of Kirk/Spock's discussion but not near the end.
My guess, oddly enough, is that the actress just stayed there and was watching the scene being filmed.
If she was meant to be there why is she gone halfway thru?
Unless she recorded the 'Let them die' thing and left when she had what she needed!