Not sure if this is actually the song the title is referencing, but I couldn't find many other Jazz songs with "greeting" in the title, so I thought I'd share it anyway.
It's called "Greetings and Salutations" and comes off of the 1975 album of the same name by Thad Jones, combining elements of hard bop, big band, and even a bit of funk, to create a fairly unique sound.
Have a listen: https://www.youtube.com/watch?v=dgrZjpdp7RI