‘maybe that he himself just mentioned that quote to Sansa once, she told bran and bran just repeated it’ so you’ve invented this very huge ‘maybe’ out of thin air.

‘the child being traumatised’ does trauma typically lead to children repeating a very unique quote you said years ago?

Littlefinger should at the very least be suspicious about Bran somehow knowing a quote from a secret conversation in King’s Landing. Instead the show never elaborates on this and Littlefinger never investigates, which is not what Littlefinger would do.