The elderly maid tells Penelope that Odysseus has returned, but Penelope is doubtful. She fears that someone has come to deceive her and does not trust Odysseus. When she sits across from her husband, she acts coldly until she orders her bed to be brought downstairs and Odysseus says how he made the bed out of an olive tree and nobody would be able to lift it. Knowing that Odysseus has returned at last, Penelope rushes to him and begs his forgiveness for not recognizing him sooner. Soon, they are recounting their stories for each other in bed and when dawn comes, Odysseus tells Penelope to stay in the house and not to speak to any visitors while he and Telemachus go to visit his father.
I think that the olive tree connects to Odysseus because everything changed rapidly around it, while the actual tree only changed very slightly. Also, the tree is the last to change, like Odysseus. Odysseus fears that the bed has been misplaced like his position as master of the house has, but finds that it is still the same as when he had left.
I think that Odysseus has successfully untangled himself because the stays firm and planted, unlike the tree that was half and half at the beginning of the poem. Which means that Odysseus has overcome his most pressing obstacles and can return to a normal family life.