The Scriptures don't tell us what Jesus and Peter talked about on that first meeting. Perhaps Peter never told anyone. I suspect they had a little conversation about Peter's actions during Jesus' trial and crucifixion. Peter had denied three times even knowing Jesus - as Jesus had predicted. And Peter was evidently not there when Jesus died. Regret and forgiveness must have been on Peter's mind. Maybe Jesus asked Peter, "Why?"
I've often thought of the differences and similarities between Peter and Judas. Both were close associates of Jesus. Both sinned against Jesus. Their sins were not too different from each other. But their actions after their sins were very different. Judas went to the Jewish authorities looking for forgiveness. Receiving none (he had not betrayed them after all), he despaired and killed himself. What if Judas had gone to Jesus for forgiveness? I believe Jesus would have forgiven him. Peter, no doubt, asked Jesus to forgive him. They must have cleared the air in that first private meeting.
For reflection: For what do I need God's forgiveness? From whom else do I need to ask forgiveness?
Let us pray. Father of Mercies, please bring to mind the actions for which I need to seek forgiveness. Help me to make amends.