Daenerys saw that forced smile, but she didn't question it. If he was perfectly willing to go along with her request, it was fine by her.
She walked along with him, keeping a hold of his arm, all the while, looking up at the sky above. How she wished she had brought her dragons with her. They would have enjoyed themselves. Instead of being cooked up all the time. How they longed for the open sky.
When Tarvek spoke to the man, she turned her attention to him, and offered him a kind smile. She nodded her head in his direction to acknowledge that what Tarvek had said was correct, but remained silent, simply observing, until he had finished speaking.
"You would have my eternal gratitude for doing us such a kindness" she added.