It looked as if she was starting to possibly give him the benefit of the doubt, and that was a good sign. He started to relax just a little, but was still confused and somewhat shocked over her reaction at seeing him. He hadn't expected that...and couldn't stop thinking about why she should be so scared of him.
Still, there would be time for those answers later (hopefully). Now was the time to seize this moment...this small window of opportunity she was allowing him. He could tell that she was not yet fully convinced of his innocent nature, and was ready to turn and run again at a moment's notice. So it was best to use this time to show her he meant no harm.
When she asked if his memory loss was true, he searched his head for the few memories he did still have floating around in there. It was all fuzzy, but there had been a name that kept pushing its way to the forefront of his thoughts.
"I..I'm not sure, but I think my name might be...Gabriel?"
He stared at her face, eager to see if this name stirred any sort of reaction.
"...and I know you're Claire. I just...I don't know how I know that. But you know who I am, don't you? Tell me, please...who am I?!"