Can atonement help ease the burden of past transgressions? Wipe the slate clean, even?
I think making ammends can help both parties move forward, so long as the ammends doesn't cause further damage. There are some incidences were it's best to leave well alone.
I suppose that in this case, you are rather referring to our own conscience about the wrongs, misunderstandings or errors committed in relationships, families, teams, groups, etc., as in our civilisations, legislation, justice systems and moral principles are, usually, defining the "rights and the wrongs", or sins and ideals, alongside with liabilities, sanctions, amends and "repairs".
Every case is special, and dealing with conflicts may require professional help, as atonement or penance alone may not allow to settle certain damages or injuries:
They are also trying a new approach within the legal and penal systems - though they will need to deepen research and investigate further, from case to case: