the act of making amends
atonement - amends
The formal noun ‘atonement’ was originally used exclusively in a religious context to express making amends with a higher power for past transgressions. In a more modern sense, it is used to describe an act of contrition undertaken by somebody to redress an offence, injury, or injustice. The verb form is 'to atone', with the same meaning implied. You might atone for something you did years ago, or a prisoner might seek to atone for their crimes.
I admired Chris’s willingness to work for a period of time without a salary as atonement for his costly mistake, but it would have been cruel and unfair of me to accept that.
The other side’s acknowledgement and apology for what happened are simply not enough. There must also be some kind of financial atonement.
Rather than pursue legal action, the firm accepted to atone for the client’s breach of contract in the form of compensation.