From the prepositional phrase off the cuff.
off-the-cuff (not comparable)
- (idiomatic) Extemporaneous; without prior preparation; spontaneous; impromptu.
- Synonyms: see Thesaurus:impromptu
He made a few off-the-cuff remarks before launching into his prepared speech.
2013 May 5, Peter Baker, Mark Landler, David E. Sanger, Anne Barnard, “Off-the-Cuff Obama Line Put U.S. in Bind on Syria”, in The New York Times[1], →ISSN:Off-the-Cuff Obama Line Put U.S. in Bind on Syria [title]
2017 June 4, Peter Baker, “Trump’s Off-the-Cuff Tweets Strain Foreign Ties”, in The New York Times[2], →ISSN:Trump’s Off-the-Cuff Tweets Strain Foreign Ties [title]
2021 October 2, John Herrman, “Will TikTok Make You Buy It?”, in The New York Times[3], →ISSN:Even when people are trying to sell you something, their messages seem off-the-cuff, like trustworthy recommendations rather than sponsored shilling.