Unintuitive is in Wiktionary and some of the Oxford dictionaries. The most widely used word with a similar meaning is counterintuitive, according to the 14 billion word iWeb corpus. The next in frequency is unintuitive, with non-intuitive and nonintuitive least used.
Unintuitive is used with similar frequency across the various English-speaking communities.
Counterintuitive is a common word in the Chihuahua word list, though it's not possible for it to be part of a puzzle unless we extend to 16-letter or 9-by-many puzzles. Since unintuitive is used a lot less often, and is absent from a lot of dictionaries, I don't think it qualifies as a common word, but it should and will be accepted as a rare word.