The case
The annual network broadcast of The Wizard of Oz was an event for every Gen X household, and Dorothy's first words in Technicolor are quoted constantly. She says she has a feeling, not that she thinks.
The quoted version is shorter and more modern. "I've a feeling" is 1939 phrasing that nobody says anymore, so the mind updates it to the way people talk.
Why our brains do this
Old-fashioned phrasing gets modernized in memory. The meaning survives; the words drift.
Sources: Wikipedia — The Wizard of Oz (1939 film) · Wikipedia — False memory: the Mandela effect
