Eleanor Shaw: The assassin always dies, baby. It's necessary for the national healing.
Eleanor Shaw: Oh, God! Where are all the men anymore? My father, Tyler Prentiss, never asked, "Is this okay? Is this okay?" You know what I'm saying, Mark? He just did what needed to be done.
Raymond Shaw: I served under him. He was a good man.
Eleanor Shaw: Well, that's what the neighbors always say about serial killers.
Senator Thomas Jordan: And you bring me rumors and conjecture.
Ben Marco: I started with nightmares. Rumors, conjectures, that's a giant leap forward.
Chosen answer: The tattooed woman was something that they all dreamt about. She was significant to the capture and the tattoos stood out among all of the other arabs.
Toolio
I always felt they were just there to cause confusion. If they started to remember the image of the Arab woman/ women would sound and look crazy trying to explain. However later in the movie when they shoulder flash backs the women were not there and Shaw choked out that other guy but, early the Arab women where there, and he had plastic on his face choking him out. So, all the memories are mixed up.