It was pretty obvious that this Patty - who she apparently looked like - was someone important to Barry. She could see it in the way he held himself and the way he needed a moment before he smiled at her. He might be trying to act as though it wasn't a big deal, but Georgina had been alive long enough to have become very good at reading people, particularly given her line of work.
She let him have the lie, even though she doubted he was all that happy to meet the doppleganger of someone he had obviously been hoping to see again. Rather than questioning him, she offered a smile back at him.
"The pleasure is all mine, Barry. I'm sorry I'm not your friend."