Oooh so many ways you can handle this...

Do they have any obligations to bad people? Have their markers called in; "Go to X location and wipe out Y group there, no questions." Y group are a bunch of pacifistic refugees who are holed up in a warehouse and are unwilling to give up their squat, but their employer needs cleared. If they don't do the research and go in guns blazing...mass conflict, if they choose to aide the refugees and not clear the warehouse their obligation increases, not to mention the ire of their boss.

Family is always a good trigger...but you don't need to kill them, or even maim them...just Take them...use them as a Hostage to make them do horrible things; whether to keep them safe or to rescue them, Remember "Taken"? 8D

Have a bad guy that likes stealing or blowing up their stuff, works best if the bad guy is someone they turned into a bad guy by their actions; ie they kill a Guard somewhere...that guards has a kid, a very smart kid, who wants revenge but isn't strong enough to face them toe-to-toe so he hits below the belt and into their pocket-books. Have him be sneaky and aim at at a relative innocent so when they catch up and get their revenge and later learnt hey were mistaken...more conflict.

Have a chase end up in a crowd of pedestrians/travelers and they have to weight harming innocents vs catching their quarry.

"Nice lightsaber you got there...be a shame if it broke..." (Don't do this to a newly-acquired Saber, that is a good way to lose a player!).

Have an epic space-battle turn out to be against the wrong people (What HAVE you got against refugeees!)...