How do Buddhists talk about forgiveness and turning the other cheek, for extreme wrong doing? How do Buddhists talk about forgiveness and turning the other cheek, for extreme wrong doing? The sorts of things that are not about being offended, not insults, but the exact opposite: are atrociously evil or wrong, so one would feel appalled if it had happened to anyone. On the one hand, one may be happy to let karma do its job, but -- on the other -- bodhisattvas must be impelled to save every sentient being.
Is the answer to seek material / earthly justice, and work to enlighten them, within the limits of Buddhist ethics?
one may be happy to let karma do its job
Recalling the brahmaviharas, I think that that -- i.e. &quot;remembering that beings are heir to their own karma&quot; -- is recommended as a recipe for &quot;equanimity&quot;.
That's possibly not &quot;good will&quot; though -- i.e. if you're &quot;happy&quot; about someone's misbehaviour, that sounds like the opposite of mudita -- and good-will is important, see e.g. the parable of the saw (as an example of Buddhist doctrine that's relevant to what you're asking).
There's also the Dhammapada verses 3 through 6 -- which recommend against &quot;he hurt me!&quot; and &quot;not stilling your hatred&quot;...
There are other topics on this site though, about social justice -- e.g. if a person lies then you might not want to believe them in future; if they steal you might tell the police...
Or one of the Zen stories is The Thief Who Became a Disciple

I gave him the money and he thanked me for it.