The whole patting jason thing sounds cute, but this is how I belive jason would respond to it.
In this alternate dimension, they are hybrids.
Bruce wayne is a dog, a German shepherd to be specific, grayson is a wolf, a Grey one. Tim drake is a dog, and damian is a black Panter.
Jason used to be a tabby cat, but after lazuras he was changed into a tiger.
When Jason used to be robin, evreyone had no problem petting him since he was a tabby cat, worst case scenario? They'd get scratched.
Now that Jason is a tiger who's not afraid to kill..this whole petting thing doesn't have an effect anymore.
Its unfortunate for grayson who used to like petting jason or play with his tail, Jason always let him, a little scared since grayson was a wolf so he never set boundaries.
Now that he can do that freely, grayson just thinks that Jason must still hate them all, whenever he tries to pet jason, he gets his face scratched and suit torn, maby even his ears bit bloody, when bruce tries..it ends in a small bloodbath, jasons claws big enough to stab him, strong enough to throw him against the wall. When tim tries, Jason may or may not break Tim's wrist, in better cases he just ends up with a few old injuries torn open. Damian doesn't even try, he knows why jason does this, as a 'cat' person himself, he knows how important personal space is, the only times you pet jason is, if he wants it.
As for the rest of the batfam, they don't get close enough to jason anyways, except cass, who doesn't invade jasons space because Jason doesn't invade hers.
How does grayson ever figure out that Jason is simply trying to protect himself? Barbara tells him, tells him how whenever he looked for jason when he was still robin- to tease him or whatever, Jason hid with Barbara, and just a couple days before Jason passed away..he told Barbara why. She never told dick after that because she didn't want to make grayson feel worse than he alredy did.
After that, grayson actively doesn't pet jason unless jason asks him too, wich can come off awkward, but it doesn't.
Because grayson is a good big brother, and jason is simply a cat.