@MonsieurFudge: They can still refuse to trust anyone outside the party and still keep to the title, especially considering they'll have to 'save the world' they will need to work together well.
Considering the history of Sem and Tiana, there's room for their past colleagues to come stirring trouble (especially that yandere girl)
Like, say, threaten to spread their past deeds around to hurt the party's reputation which by then should be more important to them than the gambling/sex they initially used to vent their stress.
Karan's case would depend on how much the asshole care about his past potentially getting revealed if/when Karan run into them again.
He can use her 'precious thing' to threaten her about it maybe.
Nick's case is the least problematic since his story has more weight in how personal it was more than the event itself, unless the guy who got him kicked get jealous about his new party doing well and try to disrupt them.