I would also add that Odysseus has in mind the tasks that Teiresias mentioned to him in Book 12. Recall that according to Teiresias, Poseidon would still be angry with Odysseus after he returned to Ithaca. Accordingly, Odysseus would have to appease Poseidon's wrath. To do that, Odysseus would have to put an oar over his shoulder and set out across mainland Greece until he came upon a people who did not recognize what an oar was. When that occurred and Odysseus sacrificed to Poseidon, Odysseus would be at the end of his labors. Thus, when Odysseus, who suffered greatly upon the seas, encountered a people who knew nothing of sea-faring, his labors would be at an end. See below Teiresias' words to Odysseus in Odyssey 12:
When, though, you have killed the Suitors...then pick up a shapely oar and travel on till you come to a race that knows nothing of the sea...And let this be your sign, you cannot miss it: that meeting another traveller he will say you carry a winnowing-fan on your broad shoulder. There you must plant your shapely oar in the ground, and make rich sacrifice to Lord Poseidon, a ram, a bull, and a breeding-boar. (A.S. Kline translation)
In order to understand Odysseus' words in book 23 of the Odyssey, one has to look at the larger context. The larger context is one of massacre. In other words, Odysseus and those loyal to him just killed all the suitors in the palace. What makes this even more pronounced is that these suitors were part of the aristocracy of Ithaca. This means that the families of the suitors will now want revenge and take steps to do so. In time, rumors of the massacre fly.
We see this take place in book 23. There is a debate among the father's of the slain of what to do next. Dolius, the father of Melanthius and Melantho say that they should do nothing, since their children deserved their fate. However, the father of Anthinous, Eupithes, states otherwise. He wants to seek revenge. So, a small army of men track down Odysseus at this father's home. In the ensuing melee, only Eupithes is killed at the hands of Laertes.
Athena comes onto the scene and stops the fighting. She makes those of Ithaca to forget the massacre and so she establishes peace.