I love the Groove...
It's a mutant hybrid of up-tempo Swing, and Jazz Waltz...
I love the movie, one of Cary Grant's last, and a major glimpse at what the first James Bond film would have been like if he had consented, when asked (by Albert R. Broccoli!), to star in it.
This was a 1964 Nominee for the Best Song oscar, and really should have won. I think the only reason it didn't was Mancini had already won the last two years running, in 1962 & 1963, for "Moon River" and "Days of Wine and Roses".