Lanfranc is one of the most eminent churchmen in all of Europe, and your personal friend. His influence at the Vatican is great. He soon returns with pope Nicholas' terms: both you and your wife are to build separate abbeys as penance for your years of "living in sin." You are to admit that you were wrong to flout the holy father, and that you have been the cause of much conflict. You are to vow to be a man of peace. When you can manage your affairs to effect it, you and Matilda are to take the pilgrim's staff and go to Jerusalem. You are to swear to be the pope's man for Normandy.
Stand your ground! How dare the pope accuse you (still!) of having lived in sin all these years. Are Matilda's and your children no better than bastards? Never will you admit such a thing to anyone, and surely not some trumped-up priest who only holds his power because Frenchmen are more powerful than the German backers of the recently deposed antipope, Benedict.
Submit yourself to the holy father's judgment. Agree to all that Nicholas demands of you: the world needs to know that William of Normandy does not always have to be right. Humility can be quite as impressive as powerful pride, when it doesn't cost too much. You can afford to be a bit humble in your powerful position now.
Your half-brother Odo, bishop of Bayeux, would make a better pope than Nicholas. (And Odo says as much, and with a straight face.) A Norman as Roman pontiff, now, that is a thought worth considering. Throw Nicholas' demands back in has face, and start using your influence to get Odo into position: Nicholas' health is failing, and there will be a new pope soon: why not your half-brother?