Hans Gruber…sitting in Holly Genero’s office…sees the TV broacast from her home.
Holly is watching with him.
The Reporter says something like:
“Y’know, your mother and father are very brave people…do you have anything to say to them?”
The little girl says:
“…come…home.”
At which point he just KNOWS that SHE’S the mother and, grabbing the picture laying flat on the table, is displayed upright, and now can see the father is John McClane.
From where does Hans gather that Holly was the mother referred to on TV?
It was definitely the expression on her face. Obviously it had to be somebody who was hostage in the building, and when Holly saw her kids on TV, her face gave it away. At least enough to make him suspicious – then seeing the family pic confirmed it.
Haven’t seen the movie in a while, but I was under the impression that Gruber knew it was Holly’s kids being shown on TV. It was when Peck said “your mother and father” that Gruber got suspicious and grabbed for the family photo.
As others have said, all the other hostages were preoccupied with being hostages—whereas Holly was preoccupied with hearing what the little girl was saying.
In the earlier scene when Holly requests a little comfort for her pregnant secretary and some groups be brought to the bathrooms, she gives a long look at the picture frame that has her family picture (but is turned over) and then stresses that she is Miss Gennero (or Gennaro, they never got the spelling of that straight in the movie). That probably made Hans suspicious.
Another possibility is that Hans overheard the conversation between McClane and Al Powell, when McClane tells Al to deliver his wife a message—and when this is all over, Al would know how to find her.
I just went and took a look at that scene on my DVD. There’s nothing that makes it logically obvious that Holly is actually Mrs. McClaine; I think Hans makes an intuitive leap based on Holly’s expression and her prior emphasis on being “Miss* Gennaro.” Hans is a complex character, which makes him one of the better movie villains (and one of the reasons Die Hard is so much better than its dozens of imitators in the years since).
Really, all that needed to happen to ruin Holly’s attempt at anonymity was that Hans had to see the picture. Hell, they could’ve written the scene so that Hans bumped into the table and knocked the frame to the floor, giving him a good look at the photo…
I think the scene, as written, just shows Hans’ ability to remember details, make logical connections, and his intuition.