The Doctor hugged Rose back, tightly. He was very happy to see her again. He thought he had lost her. More awkwardly he hugged Jack back. He didn't think it was his place to tell Rose what she had done to Jack. That was up to Jack to do, if he decided to tell her. But it wasn't easy for the Doctor to see Jack this way.
He looked at Jack at his question and comment about Team TARDIS and he nodded his head. "Right," he said. "Except I'm not sure why there are so many people here."