In that room is woman the Center has identified as a Nazi collaborator, who, as young woman, killed hundreds of Russian prisoners at the Nazis' behest. Elizabeth and Philip first must make sure - to Philip's satisfaction - that the woman in the room is the Nazi collaborator. That's what Philip insists upon before he agrees to the execution.
Elizabeth already is convinced that the woman is the Nazi collaborator. But Philip not only wants to be convinced, he's not happy with killing the woman, now a grandmother, in any case. We've seen Philip, ever since Martha, grow increasingly uncomfortable about carrying out his missions, especially when a killing is called for.
As the woman tells her story, two things become clear. The woman was little more than a child when she did what she did, after the Nazi's killed her family and terrorized her. And Philip does not want to kill her.
But Elizabeth does just that - and the woman's husband, too, to cover their tracks. And so we have the schism between Elizabeth and Philip in jagged, glaring relief.
They drive back to Washington together, Elizabeth says it's time for them to go back home - to Russia. But my guess is they'll never be able to go back home, certainly not as the couple they once were.
See also The Americans 5.1: The Theft ... The Americans 5.2: Oleg and Stan ... The Americans 5.3: Cowboys and Bugs ... The Americans 5.4: Dating, Soviet-Spy Style ... The Americans 5.5: Wrong about the Bugs ... The Americans 5.7: Gabriel ... The Americans 5.9: Gabriel and Martha ... The Americans 5.10: That Pastor, Again
And see also The Americans: True and Deep ... The Americans 1.4: Preventing World War III ... The Americans 1.11: Elizabeth's Evolution ... The Americans Season 1 Finale: Excellent with One Exception