As has been pointed out here:
In "Death in the Family," Jason does his best to obey the spirit, if not the letter, of Batman's orders:
Batman to Jason: "You stay here and keep an eye on that warehouse until I return. Take no action until I get back. I repeat, no action! Just for once, please listen to me Jason! Don't tangle with the Joker alone! Wait for me to get back, please. That madman's just too dangerous for you to handle. Do you read me?"
So, it's pretty clear that the intent of Batman's orders is for Jason to not confront the Joker without him. Jason does his best to comply with this intent, while still protecting his birth-mother. Jason seizes the moment when he sees his birth-mother alone outside the warehouse to try and get her away without confronting the Joker (obeying the spirit of Batman's orders). When she asks him to come into the warehouse, he refuses on the grounds that the Joker is in there (again, obeying the spirit if Batman's orders). He does not go into the warehouse until the [there are no expletives sufficient to describe this woman] lies to him and tells him the Joker is "long gone" and "there is nothing to worry about".
Yep. She knowingly and deliberately set her child up to be brutally murdered by the Joker. She even points a gun at him to keep him from running away. All because she was worried about being caught embezzling from the famine relief agency. I think she out-bid's Joker on evil here. He at least has the excuse of being crazy.
But Batman has no way of knowing any of this. At the time, he assumes (wrongly) that Jason deliberately went after the Joker:
Batman: "I warned you not to take on the Joker by yourself. I begged you to wait, Jason. But of course you didn't."
I can't fault him too much for this assumption. The only people alive who know about Jason's birth-mother's betrayal are:
1) [Briefly] Jason's birth-mother: She doesn't tell.
2) [Partially] Joker and his goons: Not credible.
3) [Years later] Jason himself: They don't really talk.
It seems it's this incorrect interpretation of the event - that Jason deliberately disobeying orders to go after the Joker - that gets passed on the rest of Bat-family (again see http://www.comicvine.com/jason-todd/4005-6849/forums/whos-to-blame-a-must-read-essay-on-jason-todd-697308/ for details).
This is unfortunate as it both feeds into Batman's guilt ("I should have known wouldn't wait.") and sullies Jason's memory.
What I'd like to know is, does Batman (or any of the Bat-family) ever learn that Jason' birth-mother betrayed him? I've been googling for a week now, and I can't seem to turn up a yes, or even an implied yes.
If it's a no, what do you think the reaction would be if he (or they) finds out?