How does the Catholic Church tell us to do reparation for our sins according to Church teachings?

Pope John Paul II in his apostolic letter Misericordia Dei (Mercy of God), he wrote: > 1. Ordinaries are to remind all the ministers of the Sacrament of Penance that the universal law of the Church, applying Catholic > doctrine in this area, has established that: > > a) “Individual and integral confession and absolution are the sole > ordinary means by which the faithful, conscious of grave sin, are > reconciled with God and the Church; only physical or moral > impossibility excuses from such confession, in which case > reconciliation can be obtained in other ways”.(12) > > b) Therefore, “all those of whom it is required by virtue of their > ministry in the care of souls are obliged to ensure that the > confessions of the faithful entrusted to them are heard when they > reasonably ask, and that they are given the opportunity to approach > individual confession, on days and at times set down for their > convenience”.(13) Then in Catechism of Catholic Church said: > 2487 Every offense committed against justice and truth entails the > duty of reparation, even if its author has been forgiven. When it is > impossible publicly to make reparation for a wrong, it must be made > secretly. If someone who has suffered harm cannot be directly > compensated, he must be given moral satisfaction in the name of > charity. This duty of reparation also concerns offenses against > another's reputation. This reparation, moral and sometimes material, > must be evaluated in terms of the extent of the damage inflicted. It > obliges in conscience. And in New Testament (Study Bible) Jesus said (Book of St. Mark): > 23Therefore if you are offering your gift at the altar and there > remember that your brother has something against you, 24leave your > gift there before the altar. First go and be reconciled to your > brother; then come and offer your gift. 25Reconcile quickly with your > adversary, while you are still on the way to court. Otherwise he may > hand you over to the judge, and the judge may hand you over to the > officer, and you may be thrown into prison.… So it seems like just the confession is not enough to unshackle ourselves from the slavery of sins. We have to do reparation for our sins. When I was in Catechism class before my first confession a nun from Sisters of Charity told the Catechism class Our soul is like a clean white slate when we take the sacrament of baptism. And after that when we commit mortal or cardinal sins that cry toward heaven deep dark marks are left behind on the slate. We can do fair and honest confession and then the dark marks can go away now but the marks won't be filled up as they are scratched with hurt and the slate won't look new again until we do reparation for our sins. So can anyone tell me how and in what form or ways according to the Catholic approach one can do reparation exactly as Jesus Christ talked about, the apostolic letter and Catechism of the Catholic Church referred to with some examples? I can give an example where I need to do reparation. The other day my mom was driving the car and I was at Costco parking lot with my family and she was parking the car. Now there was a car in front of us wanting to back up. There was another car just behind us. So couldn't move. We were stuck. But the front driver was honking and telling me to move from his way so he can park. We had no space to move out of the way. He was honking about 20 seconds. And was backing up though there was no space in between his car and ours. So we gave a silent honk so he stops. He came out of his, was angry and was shouting. And I got angry and was yelling at him. He was yelling again. So I quiet down finally. Let him be himself. But later I thought as a Christian I shouldn't have behaved that way. I should have shown compassion and patience. So finally he parked his car. And finally, we understood he did all that because he thought we will get his spot. So I was proved a fool. Felt ashamed also. So need to do reparation for sins after an honest confession. How does the Catholic Church tell us to do reparation for our sins?