The girl made sounds that the God of Mourning had never heard before. Sounds only dying whales would envy. Hades dealt with a lot of weeping people in the Underworld. He ignored it. Most of the time there wasn't anything he could realistically or reasonably do without compromising the rules of his realm.
But this was not his realm. She had summoned him. He hadn't summoned her. Hades could realistically and reasonably take the girl, if that was what she really wanted.
Or he could just let Hera try to handle it.
"I suppose that would be fine. But only this once." He managed to sound appropriately solemn for the first sentence, but had to quickly suppress the playful grin that came with the second. The likelihood of Hera needing to talk to another person in one of Hades' temples was akin to the likelihood of her leaving Zeus for Po.
Hades was a god of his word, and would grant the princess's request, because she had paid a price, and that was what he had said he would do. He had not, however, said when he would take her. If Hera could talk the girl into being more flexible on that point, Hades could be flexible too.