Encounter

Stranger, will you continue to be a nuisance to us through the night, roaming about the house? Will you spy on the women? Why, get outside, you rogue, and enjoy your dinner there! Either that or be smashed with a torch and go out that way!

After telling her that he once was a rich man, Odysseus says to her:

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Odysseus and Penelope

As a preparation for the killing of the suitors, Odysseus and Telemachos remove all the weaponry from the hall. Then, Telemachos went to his room to sleep and Odysseus was left behind in the hall, pondering death for the suitors. The female slaves came in to clean the hall and again Melantho is hostile to Odysseus.

Beware that you too, woman, do not lose all the glory through which you stand out among the slaves if your mistress becomes angry with you, or if Odysseus returns. There is still room for hope. And already his son is such as he was, by the favor of Apollo- Telemachos. He will be aware of any sexual play among you women. He is not longer the child he was.

Penelope overheard him and says to her:

In the course of this very month Odysseus will come home, as the old moon wanes and the new one appears.

And Penelope and Odysseus talked, Penelope about postponing the marriage to the max with all kind of tricks and Odysseus sets up a fake story, not revealing his real identity. Then Penelope asked him about Odysseus and he says that Odysseus is alive and that:

Don't think, you hussy -you shameless bitch!- that your outrageous behavior is unknown to me!.... ....You knew full well -because you heard it from me myself, that I wanted to ask the stranger in my halls about my husband. I suffer so....

The fase of the moon is now important. The prediction is that Odysseus will return at new moon. Unlike our modern calendar, the months in Odysseus' days appear to start at full moon. Homer writes that old and new moon fit within a month. Apparently his return isn't today, but the day that Odysseus will kill all suitors is tomorrow.
So, tomorrow will be the day that the new moon appears and that is the day of the feast.