This is just a guess, but I do believe that Spider-Man would drive Jason Todd and/or Damian Wayne OUT OF THEIR MINDS.
You are correct Anon. (☞ﾟ∀ﾟ)☞
I think it’s safe to say Damian would try to stab Peter.
At first, it would start off as a scare tactic “to put the arachnid imbecile in his place!”
But once Damian catches onto the fact that Peter can sense danger (not to mention dodge and bounce around like it’s nothing!) it becomes more of a game.
No matter how many knives/daggers/swords/batarangs Alfred confiscated from Damian -“we do not attack out houseguest, Master Damian,”- Damian still has at least one hidden away, and he is always ready to pounces.
Damian doesn’t understand how this boy always escapes him. It doesn’t seem to matter how much tact and stealth Damian uses, Peter always jumps away at the very last moment.
IT IS INFURIATING!
It is no longer about maiming or hurting Peter, and more about just tagging him, because Damian cannot sleep at night knowing that someone so-so infantile and untrained can SOMEHOW EVADE THE SON OF BATMAN!?!?
Damian has vowed to himself that he will at least catch Peter…he will, it would be disgraceful otherwise, and Damian cannot live with any other outcome…
Meanwhile, Peter is terrified of this child. Peter- “Why does Damian hate me so much?” Tim- “Damian hates everybody, it’s like, his default setting.” Peter- “But every time I turn around he’s there with a knife, and-and he tries to stab me!”Tim- “It’s his adjustment period, he’ll stab you and then he’ll move on.”Peter- “…” Peter- “H-has he ever stabbed you?” Tim- “Oh yeah, like a handful of times.” Peter- “And-and you just dealt with it?!”Tim- “Welcome to Wayne Manor, Peter.”
I think Jason would go back and forth with how he feels about Peter.
He would find Damian and Bruce’s irritation with the Spider downright hilarious, and he would totally make it worse- because he’s a troll like that.
The constant babble might’ve been a bit of an issue, but Jason is used to Tim’s random bouts of rambling, so he knows how to deal with it- and he knows that it’s something usually brought up by nervousness.
It might be worse if Jason actually lived at the Manor, but if he’s having one of those days, he just avoids the family anyway, so there are no problems there.
He doesn’t actually dislike Peter, at first the kid had been on cloud nine- looking at the Batcave and all their different gadgets, about to pee his pants when Batman approached him- but once the excitement and shock wore off the kid settled down.
Jason and Peter aren’t going to be buddies anytime soon- he’s a lot like Dick, and Jason can’t take Dick half the time- but the kid does seem to have a sense of boundaries (unlike Dickiebird) so maybe there’s hope for him yet…