Wait what just happened
After the disaster of a team meeting, Tony retreated off to spend some time in his lab either tinkering some more with Loki's restraining bracelets, processing all of the new information Thor had given him, or watching hours of footage of the prisoner to try and analyze some of her behavior; although now knowing that she's not human caused him to go back through past footage he had already analyzed and reanalyzing.
It was during these hours of watching security footage that Tony happened across something he found very, very interesting.
It started when he decided to go and rewatch Thor and the prisoner's interaction. She seems unbothered by their presence up until the point where Thor goes to stand in front of her. He can tell exactly when she registered Thor as her body suddenly goes rigid. He can see the disdain and distrust in her movements and even her tone.
However, the most interesting part of the footage happened after he and Thor had left. Up until this point the prisoner was very collected, stone-faced, and even when alone she showed very little of her emotions. However, this was the first break in her façade that he had seen. He watches her mask crumble as she screams and seemingly attacks the barrier. Normally he would have had the audio on, after all she is making audible noises which is uncommon enough, but listening to her screams full of anger and desperation were just too much to handle while also watching her movements. He watches her finally seemingly tire herself out and slide slowly down the back wall in a way that seemed defeated and exhausted.
Just when he was about to turn the footage off to revise his notes, something very interesting happens, reigniting Tony's curiosity. Tony watches, intrigued as none other than Sergeant Barnes hustles his way into the room as if he were hiding from someone.
If he remembers correctly, Tony remembers Rodgers and Barnes having an argument that morning as he had made a "trouble in paradise" type comment that Tony found very funny but no one else did. Perhaps that added to Steve's mood during the meeting. Oh well.
The prisoner doesn't react much to him besides becoming a bit on guard as she did every time someone entered the room, but then she did something very interesting. She looked at him. She looked at him not in the way that she looks at everyone else where she is seemingly not registering that someone is in front of her, lost in her own world. She looked at him like she was taking in every detail of the man who was now sitting in front of her. Her mask seemed to slip once again, but instead of the distrust or the anger she showed earlier, she seemed intrigued. That intrigue quickly turned to surprise as Barnes begins speaking to her.
Tony scrambles to get the audio turned back on and is astounded by her receptiveness.
Barnes tells her his name and something in her face leads Tony to think that she may have registered some of what had been said. His theory was confirmed when Barnes was leaving and she walked up to the glass again and uttered her second word of the day, or ever, "James". Tony would deny it if anyone asked but he whooped in excitement at her speaking again. That's twice in one day! In all the weeks that she had been in the tower she had never said a single word, and within the span of this one day she had spoken twice!
Clearly English was not a language she was familiar with, her attempt at repeating Barnes' name was nearly unrecognizable with her thick accent from whatever her first language was, but her attempt was at least recognizable enough to be able to know what she tried to say.
Tony was elated, there was so much to do with all this new information. He had to talk to Thor, he had to talk to Barnes, he had to try and talk to her, he needed to rewatch all of this, take new notes, theorize, etc., etc., etc.. there was just too much for him to do. Just as he began to rush off to begin his new list of tasks, he realized there was one thing he needed to do before anything else.
"Jarvis, lock the door to the cell room"