Yes, Walter interprets the white tulip as a sign from God that he can be forgiven, by Peter as well. (I'm assuming that the dead body with the exotic gadgetry in it was somehow not a Fringe case the year before. Which I suppose is why Weller thought the letter needed to wait a year, though I don't know how he could know that.) But if Walter was now planning to tell Peter, why is it necessary to burn the letter?
I believe Peck's wife died 10 years ago, which would be before Fringe Division was created, yes? But, even if it was 1 year ago, all they'd have to go on was a weird ass autopsy report, since none of Peck's timetravel research existed yet and no one died by energy drain. With just the body, there's nothing to investigate.
Whatever the case, Walter was clearly ready for the sign at the time of the Peck/Walter convo, but since that never took place in the new timeline, Peck postponed the message until then.
And Walter burned the letter before getting his sign from God that it would be OK to speak with Peter about what he'd done. He doesn't need a letter now anyway. He can just talk to him.
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I love timetravel stories and I thought this one was particularly well done. I wish they'd addressed what happened to the Past Pecks, but I suppose, since the train wasn't crowded with them, he was annihilating his past self with every backstep.
Also cool to see RoboCop ironically turning himself into a cyborg. Peter Weller's a good actor, too. He can do good, evil and conflicted. I enjoy seeing him get work like this and 24.