I mean he was in Arkham Asylum. Couldn't his relatives have been targeted or did they just not talk about him since he was going to be in the next arc?  It could have been cool because, unless the White Knight only targeted blood relatives, Bruce Wayne and Dick Grayson could have also been targeted by the White Knight since he was adopted by Bruce which would also make Dick his brother.

@SpaceCommander: The thing is, no one other then the Bat family actually KNOW that it's Jason in Arkham. The White Knight wouldn't have been able to figure it out.

Though they did seem to leave out some of the inmate's relatives…notably Scarecrow's, as they've actually been featured in stuff before.

I thought about that too, but didn't some of the inmates' relatives changed their names.

@SpaceCommander: Yeah, but that shouldn't have mattered…White Knight found Mad Hatter's relatives, and they had changed their names.

Oh, well I thought he just had some weird super-power where he can figure out villains' relatives since he found Mad Hatter's relatives even though they changed their names.  But I'm he guessing he doesn't actually have that super-power since he didn't target Bruce or Dick.  By the way, I only had the theory about said super-power because they didn't really seem to explain how he found out about the Mad Hatter's relatives.

Jason Todd is dead to the world but his finger prints have also been burned off so there is no way to identify him that way either.

@RedHoodJT: 
His fingerprints aren't burnt off, they just can't be indetified. Anyone in the Batfamily has had their fingerprints removed from every database in the world, minus the bat-system.

He's John Doe to them. Just the Red Hood.

Well the notion they have "no prints" on file anywhere is ridiculous.  Didn't Bruce get booked once for murder? Arguably they all go to the DMV too. 

In the case of Jason, he had records. i mean in theory they could hack all the major databases but we know Jason's been to juvie, there are paper records with his arrests and  likely prints before he became Robin. Though those would've been sealed when he turned 18, no idea what happens to that stuff when a kid dies before that, legally. We do know child services followed up Jason's death years later. But in his case, you also have to imagine Batman burglarizing police stations and government agencies to accomplish that  as well.
There has to be altered prints in a lot of places. It's a can of worm issue if one thinks about it but the blanket "no prints" statement probably should be "no real fingerprints anywhere on earth"

There is also the simple fact that Jason didn't have any blood related family alive.