[She appreciates that Ezra is taking it seriously, and willing to listen. If he had signed any other name, she would've maybe found it a bit funny and instead spent her time teasing Han for being jealous of someone he's never actually met, but signing Jabba is different, and she doesn't want him upset by that.]

Han used to smuggle for Jabba. He owed Jabba repayment for a shipment he had to dump, but was... late in repaying it.

[Or just that he never repaid it. Both work.]