Failure to Communicate - S2-E10
Continuity mistake: When the scene starts with Stacy and House in the airport about to start talking, she has a pen in her mouth. In the very next shot it's on her ear, and in the next it's gone. It switches back and forth throughout the rest of the scene.
Answer: She would have No Reason to know it belonged to the CIA. If she did know he went off in the helicopter, all she would know is that it wasn't an ambulance helicopter.
Greg Dwyer