"You're locked out?" The question's there just to make certain that Peggy's understanding the gesture correctly, but if she is that would definitely explain what he was doing. Picking the lock because he'd managed to leave the key on the other side of the door. Poor thing - and he might not have ever had to do it before.

"Is there anywhere that you could get a new key?" Uncertainties about how Peggy had gotten there aside she couldn't just leave him to struggle at getting into his room, and maybe if she did help him he'd be able to help her - at least to show her someone that could help if he couldn't explain it himself.