Liz Holmes inadvertently stumbles upon the cure, vindicating her reputation.

She will be given a clue for the cure, she stumbles upon it, but nobody believes her this time. Time stone is used to rewind all the way back to 2003 in a third attempt

The Time Stone can't be used to "rewind" anything. Did you not listen to the 10 minutes of exposition by multiple characters on the truth about how time works?

And yet they used it that way at the end of infinity war.

Not to rewind. Rewind implies changing something in your own past, but nobody's past changed. Only the futures of different timelines, if that makes sense.

They made a big deal about that for a movie, considering it is all fantasy. It’s a distinction without practical meaning for storytelling purposes. Just to avoid the scene where Marty sees his own foto fade. They could have just ignored it.

A good way to think of this is a git checkout from anywhere . And then all future commits happen in a branch / detached head state, not affecting the place you checked out from i.e. original timeline.

They made a big deal out of it in the movie, that the stones had to be returned to the exact time they were taken from, or else they would be changing the future of the old "head".

That was exactly how it was used in Doctor Strange. It's just a movie, they play fast and loose with the rules all the time.

Tony Stark then snaps his fingers...