The Doctor had nothing to say to that. He felt as though something had caught in his throat. He was taken aback by how casually Rose had relayed the information, how at ease she seemed to be with the idea of someone with her face doing ... that. She seemed to relish telling him about the relationship the character had with someone who had his successor's face, and it hurt. How could it not? He would rather it have anyone else, anyone but a man who looked like his replacement.
When she stood, it took him a moment to follow suit. He felt more lost than ever. You deserve this, he thought. After all the things you've done. You gave her up, and she moved on without you. You don't have the right to be part of her life anymore. It was only Rose's generosity, her genuine kindness, that had brought her here. Not him. Not any ties between them save, perhaps, the coincidence that she happened to know him.
He was silent, getting into the cab. There was nothing else to say.