I have a memory of reading an article about Tom Paxton many years ago in which he was quoted as saying that when he heard Dylan sing Don't Think Twice he thought it was an unbearably cruel song and Last Thing On My Mind was his reply to it, what the woman "who just wasted my precious time" might have said.
That is what I remember but my memory may be playing false and I would be delighted if someone could confirm it or correct it.