Tyrion is in his tiny bedchamber, which is much smaller and less ostentatious than the suite he had as the Hand of the King. He's going to complain about that a lot, so just pretend I mention it after about every other sentence. He looks at his reflection at his new facial scar. It's not all that big, frankly. And then! Cersei knocks on the door. She explains that it's "your sister. The queen?" I'm not sure she should still be queen, since her husband died. Certainly once Joffrey gets married, she should stop calling herself that. Tyrion is reluctant to let her in because she has two knights with her and he's pretty sure she tried to kill him. She convinces him to unlock the door by suggesting that if she were really consumed with the bloodlust, a locked door would keep her out. Tyrion grabs a convenient axe and lets her in, although he keeps the knights locked outside. At this point I'd like to call back a joke I made in Season One, where I mentioned that axes are the traditional weapons for dwarves. I stand by that joke!
Cersei claims that the reason she's here is that she wanted to see Tyrion's face. Contrary to popular rumor, he has not lost his nose. This is a reference to the book, where Tyrion does, in fact, get his nose cut off. Tyrion is also constantly being referred to as an ugly, twisted dwarf, which doesn't really work for the TV show, what with Peter Dinklage being a very handsome man. So instead of having his whole face chopped up, our Tyrion is just going to end up with a rather dashing facial scar. Cersei needles Tyrion about how the key to victory was their father Tywin riding in with an army, rather than Tyrion's diabolical plans. Even though Tyrion led an attack after Joffrey ran away, he doesn't get any of the glory. Tyrion brings up the fact that his face was split by someone who was actually supposed to be on their own side. Cersei cheerfully ignores this, which is something she'd do regardless of whether she'd been trying to assassinate him.
Finally, she gets to the point: she wants to know why Tyrion is going to meet with their father. Tyrion plays dumb: "He's my father. Do I need to want something?" On one hand, he's right. Why shouldn't he go say hello to Tyrion? But in reality, Tyrion obviously has something going on because that's who he is and that's the show we're watching. There's much sarcasm as Tyrion talks about how Tywin surely loves him very much but hasn't come to visit him even once. Why, he asks, does Cersei care? Well, she says, he's slandered her to father before. Like when she had a nine-year-old girl beaten until she lost an eye. Cersei thinks it's not as bad as it sounds because she was a nine-year-old girl herself at the time. Tyrion goes with the standard defense of "It's not slander if it's true." Cersei still probably doesn't want someone tattling to Tywin about just how bad Joffrey has been as king. Cersei says, "You're a clever man. But you're not half as clever as you think you are." Tyrion takes a moment to savor a good setup line, and then crushes her: "Mmm. Still makes me more clever than you." Zing! It turns out the actual weapon of choice for dwarves is witty repartee.