Thank you for this expert character sketch which is right on the mark. Finch surely was testing Carter in this scene, seeing if she was daring enough, astute enough, reckless enough to do the work he and Reese have set for themselves. She passed the test, as you show, by not backing down.

During that scene, I was also mindful of Reese's plea to Finch, " Look out for her for me.". I wonder, if in his own way, Finch was doing Reese's bidding too. I like that your story has pushed me to think again about this pivotal moment in the show.