My influence with HK is at 100, but there is only one possible lesson for killing Jedi. I think you were mistaken about the rewards. Here is why. When you ask him about killing Jedi "I need to know, to protect myself.", he begins to tell you what weapons to use. Follow that dialogue tree to it's end, "What do you mean?", and you get the Wis bonus and Will save bonus. Then ask, "You seem to have thought this through.", and you get the Constitution and Reflex bonus. That is it.
You only get +1 Wis, +1 Con. Not +2 of each. Either that or the dialogue tree is not coming up for lesson #2. If you could show me a dialogue script for what I am missing, if anything, or take some still shots of dialogue for a second Jedi lesson, I would be grateful.