The scene seemed pretty straightforward to me.
Henry saw the light coming from the door and found the key, (which I must admit was pretty cool, despite how random it was that he was sitting where he was). He found the key and slipped it into his pocket just in time before the others saw (because convenient timing is convenient). Then he handed over the page, knowing that he had to play along in order to protect himself and his mother, but also knowing she would do her utmost to undermine the badguys while only pretending to work with them, (her threatening the others was a sign to Henry that she was still on his side despite what was happening). And he was able to hand the page over because he knew it’d do them no good because he had the key, which they don’t even know they need.
I’m glad Henry’s finally getting something to do.