Seeking Forgiveness from Someone Called a Mamzer

I called my friend a mamzer, and his parents have passed away. Do I need to ask for their forgiveness at their graves?

You do not need to ask for their forgiveness. If you said 'mamzer, son of a mamzer' and insulted them during their lifetime and then they passed away, if they are buried within 12 kilometers, you should bring ten people, go there barefoot, and say: 'I have sinned against the God of Israel and against this person buried here.' If they are buried far away, you can send a messenger there. If you said this after they died, apologize in the place where you shamed them.

Shulchan Aruch, Orach Chaim, Siman 606, Section 3: "If the one he sinned against has died, he brings ten people and stands them by the grave and says: 'I have sinned against the God of Israel and against this person whom I have sinned against.'" In Mishnah Berurah, there, Section 13: "If he called someone a mamzer, it is said that he also insulted the honor of his parents and must go to their grave, but many disagree, saying he can claim he did not intend it to affect the parents unless he called him a mamzer, son of a mamzer." In Section 14 it is written: "And he must go there barefoot. If it is beyond three parsahs, he may send a messenger, and the messenger will take ten people and go to the grave and ask forgiveness on behalf of the insulter, saying: 'I am the messenger of so-and-so, who publicly acknowledged that he sent me to say that he sinned against the God of Israel, etc.' If he insulted after death, he does not need to go to the grave but asks forgiveness in the place where he insulted." A parsah is 4 mils, and each mil is approximately a kilometer, so 3 parsahs is 12 kilometers.