What myth were they talking about in chapter 15?

It looks like you may be referring to what Annabeth calls the "three-thousand-year-old gossip" of Ares and Aphrodite's love affair. That would be the closest thing to a referenced myth or legend in Chapter 15.
According to Greek myth, Aphrodite (the goddess of love and procreation) was well-known for her many affairs with both men and gods. Her luscious beauty often caused great rivalries among the gods. Many fought to possess the beautiful goddess. To quell the rivalries, Zeus married Aphrodite off to Hephaestus (the god of smiths).
However, Aphrodite was dissatisfied with the marriage, and she sought comfort from other lovers. Aphrodite's most secret and passionate love affair was with Ares (the god of war). Their children included Eros (the god of love), Phobos (the god of fear), Anteros (the god of counter-love), Deimos (the god of terror), and Harmonia (the goddess of harmony).
In Chapter 15, Annabeth mentions that Hephaestus is always trying to embarrass Ares and Aphrodite. In other words, he enjoys exposing his wife and her lover in the act of adultery. Annabeth's account is corroborated by Greek myth, which tells of Hephaestus chaining Ares and Aphrodite to a bed in his chambers. At the time, Poseidon (the god of the sea) stepped in to help the beleaguered lovers. Aphrodite was so grateful for Poseidon's help that she had an affair with him. This is why Ares (in Percy Jackson and the Lightning Thief) tells Percy that he and Poseidon "go way back."
 
https://www.greek-gods.org/olympian-gods/aphrodite.php

https://www.theoi.com/Olympios/AphroditeLoves.html