It doesn't make complete sense, but Peter already was existing in a timeline in which he didn't exist before the reset. When Peter stepped into the universe machine and bridged the two universes he disappeared and a new timeline began.
So he was never actually saved by Walter in that timeline and the timeline in which he was saved by Walter had already been erased.
This is what I gathered as well. Essentially Peter is the "original" paradox that still exists... or can exists because of some weird quantum entanglement or whatever.
One huge detail that is very odd is the fact that invasion has happened in the perpetual now in 2036, but yet there is the future of 2609 practically unchanged... like it's just a different place on the map Windmark can visit anytime.
Unless there is some sort of theory for this, perhaps involving the very important year of 2161, this is the biggest thing that doesn't make any sense.
Otherwise a great finale! Some very moving moments and a very fitting "end" for Walter. This time he took a boy through a portal to save the world and obviously succeeded, pretty much redeeming himself.