How will the non-Muslim take his right on the Day of Judgment from the Muslim who wronged him, knowing that the Muslim's good deeds will not save the non-Muslim from Hellfire?

The Day of Resurrection is a day of justice and recompense, where no one will be wronged. Grievances between people, both believers and disbelievers, will be redressed, even for a mere slap. Retribution will be exacted through good deeds and sins. As for how retribution will be exacted from a wrongdoing Muslim for a disbeliever, that knowledge rests with Allah. We believe in Allah's justice and His delivery of rights without delving into the details of the unseen. If seeking forgiveness from the disbeliever is not possible, one should supplicate for their guidance and give charity on their behalf.