Hodor was already Hodor. It's not like there's a timeline 'A' which is linear and we have a perfectly fine and fully cognitively functioning Hodor. Then event 'B' occurs which is traveling back in time and then we get new altered timeline 'C' (i.e., a mentally challenged Hodor whereas he was perfectly fine before we went back in time).
He was always going to become Hodor. It's the sort of fate/predestination angle of time travel. The event has already happened in the past. We finally just saw what happened that made Hodor, Hodor in the present. The other side of that coin is since it already occurred in the past -- the traveling from the future/present HAS to happen too. Unbeknownst to Bran, he was always going to fukk Hodor up.
You saw the last don was like, "Listen to your friend," when Meera was telling him to warg into Hodor. He wasn't even tripping
. It was always going to happen. There's no set of events that could have transpired where Bran didn't warg into Hodor and subsequently fukk him up, because that past reality had already occurred and been realized.
It's Bruce Willis seeing adult him get killed in 12 Monkeys in the train station as a kid. It's trying to alter events and unknowingly creating those same events you were trying to prevent in the future.
The ink is dry.