I've always thought of the woman as Janice whether the credits say so or not. It's a nice touch and makes sense given her facial expression and body language. She shakes her head as if to say, "What the hell have they gotten themselves into now?" Whether she knew that Spock had died isn't clear, but she clearly has the look of someone who knows the people on board the ship.
Thats the way I've always interpreted that scene. It's the same same look a mother gives to her kids when they come in covered in mud