"The Jason Thing" is a secret that Jenna and Garrett fear the girls will find out. It is not revealed what it is until "Over My Dead Body," when it becomes clear that Jenna and Garrett slipped Jason a note the night or morning after Alison went missing that said, "I know what you did" leading him to question whether he murdered his own sister while under the influence.
For a full year after Alison's death, Jason questions whether he killed his own sister, keeping the note with him. He vigorously questions Spencer after he hears that she claimed that Ian confessed to killing Alison; such information would vindicate him if it is true, so he is very invested in verifying the claim. However, Spencer's vague answer leaves him wholly unsatisfied. He never told anyone about the note until Aria Montgomery approaches him at Ian's funeral in "The Devil You Know." She is speechless and confused, but promises not to tell anyone. He can finally breathe a sigh of relief that he didn't kill his sister.
Although Jenna and Garrett did not explicitly refer to "The Jason Thing" as such in the midseason finale, it is clear that this is what they meant, as I Marlene King has revealed in an interview that "You’ll find out what "The Jason Thing" is in the [mid]season finale."