After the slaughter of the suitors, Odysseus warns his son that they should be wary of their families seeking recompense.

Odyssey 23.118–122:

“For whoever has killed only one man in his country,
one who does not leave many behind to avenge him, flees,
leaving his relatives and his paternal land.
And we have killed the bulwark of the city,
the best by far of the young men in Ithaca.
I order you to think about these things.”

καὶ γάρ τίς θ’ ἕνα φῶτα κατακτείνας ἐνὶ δήμῳ,
ᾧ μὴ πολλοὶ ἔωσιν ἀοσσητῆρες ὀπίσσω,
φεύγει πηούς τε προλιπὼν καὶ πατρίδα γαῖαν·
ἡμεῖς δ’ ἕρμα πόληος ἀπέκταμεν, οἳ μέγ’ ἄριστοι
κούρων εἰν ᾿Ιθάκῃ· τὰ δέ σε φράζεσθαι ἄνωγα.

This passage makes me think of Ajax’s words to Achilles in book 9 where he seems to imply that payment may be rendered in the situation of a murder.

Il. 9.632-638:

“You are relentless: someone might even accept payment
for the murder of a brother or the death of his own child.
and after making great restitution, the killer remains in his country,
and though bereft, the other restrains his heart and mighty anger
once he has accepted the price. But the gods put an untouchable
and wicked rage in your heart over only a girl…”

νηλής· καὶ μέν τίς τε κασιγνήτοιο φονῆος
ποινὴν ἢ οὗ παιδὸς ἐδέξατο τεθνηῶτος·
καί ῥ’ ὃ μὲν ἐν δήμῳ μένει αὐτοῦ πόλλ’ ἀποτίσας,
τοῦ δέ τ’ ἐρητύεται κραδίη καὶ θυμὸς ἀγήνωρ
ποινὴν δεξαμένῳ· σοὶ δ’ ἄληκτόν τε κακόν τε
θυμὸν ἐνὶ στήθεσσι θεοὶ θέσαν εἵνεκα κούρης
οἴης….

The scholia to the Iliad contend that Ajax is referring to an actual practice.

Schol. bT ad Il. 9.632-33a

“For it was the custom to give [recompense] to the relatives in order to go into exile for not more than a year…

ἔθος γὰρ ἦν τοῖς συγγενέσι διδόναι πρὸς τὸ μὴ πλέον τοῦ ἐνιαυτοῦ φεύγειν

One might wonder why Odysseus does not think it fit to offer recompense to the suitors’ families…