none of this makes any sense, as you would presume the pickpocket on the bus was Silk. If that was the case how did Birds get it from Silk?
I don't presume, I know, because Tintin's wallet, stolen by Silk, is later returned following his encounter with the Thompsons when he tries to steal a wallet but is prevented by an elastic band. The Birds never got it from Silk but when they searched Tintin's flat following his kidnapping.
The only connection between Silk and the Birds is that he stole Max's wallet containing his parchment and Sakharine's.
Let's see if we can go through this step-by-step:
Parchment #1 is found by the Birds in a model of the Unicorn at Marlinspike.
Parchment #2 is found by Tintin under his desk of drawers, having fallen out of the model he bought from the market. It is stolen that same day by Silk on the bus.
#2 is recovered and returned to Tintin after the night time encounter between the Thompsons and Silk.
Parchment #3 is stolen by Barnaby from Sakharine and given to the Birds who now have #1 and #3.
Max Bird is in town with #1 and #3 in his wallet which is stolen by Silk, but Bird suspects Tintin is the thief.
The Birds have Tintin kidnapped and his flat burgled. #2 is found and given to Max, who keeps it during his getaway from Marlinspike.
Silk is arrested by the Thompsons. Tintin finds Max's wallet with parchments #1 and #3.
Max is arrested before he can cross the border. #2 is returned to Tintin who now has all three.
I hope this clarifies things.