ok, so if we accept that new rule, there is a specific timeline that you can never change.
What this means is that, even if you don’t travel in time, you can never change your own future (since the timeline is already “set in stone” as you say). I think this in itself is important, because you automatically take out the “free will” factor. It is a religious and philosophical discussion as much as anything else, and results in a fatalistic view of the world.
As far as time travel is concerned (and this rule is used in most sci-fi movies that deal with time travel), this again would mean two things: either that whatever you do is irrelevant and wiped out from history, even if it creates a temporary parallel universe (what Terry Pratchett calls a “realtiy bubble”), or, more commonly, you do whatever you were meant to do, and become part of a history that you were already a part of to start with. So, even if you try to change history, what you’re really doing is what you were supposed to have done all along.
In the latter scenario, either your grandfather is invinsible no matter what you do (because history said he lived so all of your efforts to kill him will fail and be documented as near misses in his life), or you do manage to kill him, but it turns out he was never your grandfather in the first place, because the guy who actually got your grandma pregnant was that other boyfriend your parents didn’t tell you about. Or even you.