Jason would visit your house on a daily basis to get you to tend to his wounds, no matter how minor they were. At this point, it was practically a routine. Only to see you, that's why he did it. Regardless of whether he was the Arkham Knight or not, you treated him equally.
He was about to pass out when he first encountered you, so he accepted your offer of assistance even though he wanted to decline because the Arkham Knight shouldn’t need help. He was taken aback by your kindness. He had developed somewhat of an obsession with you ever since that day because he knew you saw him in a way that no one else did.
He was seated on your couch, with an awful wound on his torso, and he had taken off his armor, including his mask; this was the first time he had revealed you his face. He didn't even flinch when he noticed you inspect his clean; he simply observed you. He enjoyed observing your face, those green eyes of his were analyzing you and drinking you in like a thirst. He was amused by how gentle you treated him; it felt good being pampered. “You’re good at this” his rough voice broke the silence.