How can he seek the forgiveness of one who has died?

Praise be to Allah.

Since your grandmother has died and gone to her Lord, you cannot know whether she has forgiven you or not. There is no way that you can ask for her forgiveness now that she has died. This confirms the importance of the hadeeth of the Prophet (peace and blessings of Allaah be upon him):

Whoever has wronged his brother with regard to his honour or something, let him ask him for forgiveness before the time when there will be neither dinar nor dirham, and if he has any good deeds it will be taken from him in proportion to the wrong he did, and if he does not have any good deeds (hasanaat), some of the other person's evil deeds (sayiaat) will be taken and given to him to bear.

Ibn Hajar (may Allaah have mercy on him) said in his commentary on this hadeeth:

Whoever has wronged his brother i.e., if he has done something wrong to his brother.

with regard to his honour or something i.e., anything else this includes all kinds of wealth and wounding, even a slap in the face and so on. According to a report narrated by al-Tirmidhi, with regard to his honour or his wealth.

Before the time when there will be neither dinar nor dirham i.e., the Day of Resurrection.

Some of the other person's evil deeds (sayiaat) will be taken i.e., they will be taken from the account of the person who was wronged and given to him to bear i.e., they will be added to the account of the wrongdoer.

Muslim also narrated a hadeeth similar in meaning to this through a different isnaad. This version is clearer in meaning: The one who is bankrupt among my ummah is the one who will come on the Day of Resurrection with prayer, fasting and zakaah to his credit, but he will come having slandered one person and shed the blood of another and wrongfully consumed the wealth of a third, so (his victims) will be given some of his hasanaat (good deeds), and if his hasanaat run out before the score is settled, some of their sins will be taken and thrown onto him, and he will be thrown into Hell.

According to a report also narrated by al-Bukhaari from Abu Hurayrah, the Messenger of Allaah (peace and blessings of Allaah be upon him) said: Whoever has done wrong to his brother, let him seek his forgiveness, because in the Hereafter there will be no dinar or dirham, and let him ask for his forgiveness before some of his hasanaat are taken and given to his brother, and if he has no hasanaat, some of his brothers sayiaat will be taken and thrown onto him. (Reported by al-Bukhaari, 6053)

Abu Naeem reported from Ibn Masood that a person will be taken by the hand and made to stand before all of mankind, and a caller will cry out: This is So and so the son of So and so. Whoever is owed anything by him, let him come forward. So they will come forward, and the Lord will say, Give them what is due to them. He will say, O Lord, the world is finished, so how can I give them anything? He [Allaah] will say to the angels, Take from his righteous deeds and give each one what he is asking for. If he is to be saved and there is even a mustard-seed worth of his hasanaat left over, Allaah will multiply it until He admits him thereby to Paradise.

Ahmad and al-Haakim reported from Jaabir from Abd-Allaah ibn Unays, who attributed it to the Prophet (peace and blessings of Allaah be upon him): No one of the people of Paradise will be allowed to enter Paradise when one of the people of Hell has been wronged by him, until I settle the score, even with regard to a slap in the face. We [the Sahaabah] said: O Messenger of Allaah, how will that be, when we will be gathered barefoot and naked? He said, By virtue of sayiaat and hasanaat.

In any case, you have taken a very important step, which is repenting to Allaah. If you sincerely repent to Him and do as much as you can to honour your grandmother (for more details, see Question #763), and she sees in her record (on the Day of Judgement) that you sought forgiveness for her, perhaps she will forgive you on that Day if she had not already forgiven you in this world. Make lots of duaa for her. May Allaah forgive us all.