Outside, Jin is being the best doorman in the world, opening the door for an exiting businessman. A horn honks, and Jin rushes to the street to open the car door for Jae, pulling up in a silver BMW. "Good afternoon, Mr. Lee," says Jin, and Lee looks at him and gets out of the car without saying anything. So I figured that here was when we see Jae Lee turn out to be a spoiled rich dick who's all wrong for Sun, but then just before going inside, he spots the flower on Jin's lapel and asks if he can borrow it, as he has a date. Jin says "of course," and unpins it and hands it to Jae, who admires the flower, which looks much like the one that's such a big honkin' deal to Sun and Jin's relationship. Jae asks Jin's name, and thanks him, calling him "Mr. Kwon." Jin looks like he likes the sound of that.
Inside, we see that Jae's using the flower as his own boutonniere, so while he might not be a completely spoiled rich dick who's all wrong for Sun, he's certainly not as thoughtful as Jin.
Anyway, he's telling an uproarious story that revolves around being locked out of his hotel room wearing only a towel, and don't you hate it when the maid doesn't believe that you own the hotel, and haven't we all been there? To his credit, he does tell the story like he's not boasting. "I can't believe how normal you are," she says. "I think you're great too, Sun," he says. Uh, that's NOT what she said, Captain Ego. She laughs bashfully. Then he says he'd like for them to keep seeing each other. "Our parents will be so thrilled. No more matchmakers. No more pressure. We can be free." Sun looks thrilled, so it's time for the bombshell. "Can I tell you a secret?" he asks. Of course, she says, smiling. To be honest, I thought he was going to tell Sun he's gay and that he wanted to keep seeing her as cover. Turns out I was half-right; he wants to date Sun as a cover, but it turns out that he met an American (woman) when he was at Harvard. He hasn't told his father yet, but in six months he's going to move to the U.S. and marry her. Sun does her best to keep the smile plastered on, but it falters a bit. Jae notices: "Wait you didn't think " but Sun interrupts him and says, "Of course not," and then, "America. That's wonderful." Jae's confused. "I thought you " Interrupted by Sun again: "I'm very happy for you."
So then they're interrupted by what appears to be the manager who hired Jin, but we only see him briefly, so I don't want to swear to it. He's obviously a lot more deferential than he was when he was interviewing Jin, but that would be due to knowing who Jae was, which is another reason why I think it is him: he came over to suck up. He asks Jae if there's anything else he needs, and asks Sun if she would care for some coffee or dessert. They're both fine. In fact, Sun's gotta take off, as she has an appointment, and it certainly has nothing to do with Jae's revelation! He clearly thinks it does, but she doesn't really give him a chance to say anything, brightly smiling and thanking him for lunch. She walks out, and with her back to Jae she's free to look as hurt as she feels.