1459 Many sins wrong our neighbour. One must do what is possible in order to repair the harm (e.g., return stolen goods, restore the reputation of someone slandered, pay compensation for injuries). Simple justice requires as much. But sin also injures and weakens the sinner himself, as well as his relationships with God and neighbour. Absolution takes away sin, but it does not remedy all the disorders sin has caused. Raised up from sin, the sinner must still recover his full spiritual health by doing something more to make amends for the sin: he must "make satisfaction for" or "expiate" his sins. This satisfaction is also called "penance."
(Cathechism of The Catholic Church)
The forgiveness of sins has four steps:
Step 1: Repentance of sins
Step 2: Seek forgiveness of sins
Step 3: Sins are forgiven
Step 4: Make some atonement for the temporal punishment due to sins already forgiven.
Note this is not atonement for the eternal punishment for sin (Jesus has paid that in his blood) but for the temporal punishment due for sin, though punishment may not be the best word for it.
Non-Catholics accept steps 1, 2 & 3 but seem to reject step 4. Yet making reparation/ restitution/ atonement for our sins is necessary for both justice and for our own perfection.
There is a Biblical example of penance as part of repentance.
In Luke’s gospel there a thief called Zacchaeus who was a chief tax collector and became wealthy overcharging on tax. One day he met Jesus and had a massive conversion. He said "Behold, Lord, the half of my goods I give to the poor; and if I have defrauded any one of anything, I restore it fourfold."
And Jesus said to him, "Today salvation has come to this house (Lk 19:8-9)'