Countess Lydia, having told Karenin that Anna and Vronsky are in Petersburg, takes him into her sitting room and shows him Anna's letter requesting to see Seryozha.
Karenin is willing to let Anna see her son, but Countess Lydia persuades him that's a bad idea. She appeals to his vanity. She tells Karenin that he is lofty and that Anna is base. Her request is only cruelty to Karenin. He agrees that Anna should not see Seryozha.
Countess Lydia deliberately pens a very cruel letter to Anna in French, a language that she uses frequently (see our Character Analysis for thoughts on why). The letter offends Anna entirely.
Karenin goes home feeling very uncomfortable. He can't concentrate on anything, and remembers his cold, formal conduct with Anna in the aftermath of her confession of her love of Vronsky.