"Jeongmal gamsahabnida," Jae said with a bow of her head, politely thanking him for wanting to help. If he could help her, she'd be grateful to him for that. The idea of having Eunji back was a guilt that Jae felt she'd carried for a long time. Too long. She didn't just want to free Eunji to rid herself of it (because she was sure that Eunji would be angry at her for getting her trapped there in the first place), but to know that she'd been able to finally get someone to free her. Only then could Jae really atone for what happened.
He released her and Jae reached forward, pulling him into a hug, thanking him again in her native tongue. With another bow, she made a hasty exit. Hugging him was taking a chance as it was, but she felt it was the best way to show her appreciation for what he was offering to do for her.