The scarf was in a bag when they were all in a pub when Ollie demanded they went swimming, it can clearly be seen on the seat beside Tony.
After swimming when entering the bar, Ollie is carrying a bag over his shoulder, and a snorkel pipe thing and small inflatable orca in his hand. He is wearing a green tshirt, thin hoodie thing (unzipped) and shorts (no scarf).
After Ollie disappears, Tony goes outside the bar and finds the bag, snorkel pipe and orca on the ground.
I am pretty sure now that this isn't a continuity error (it would be a major clanger, especially as they went to the trouble of showing the scarf in the pub earlier). Ollie wasn't wearing the scarf. Tony has forgotten this. I think he may remember soon. Someone has seen the picture of Ollie wearing the scarf in the picture taken that day and assumed he was.
I cannot fit this into a theory (especially to relate it to how it was in the basement, how it ended up in a charity shop with extensive records and how it happened to clearly be in a picture that Silvie face booked and Tony saw. We all thought it was a bit of a massive coincidence that the scarf was so easy to trace... Maybe it was meant to be found).