The most common and most likely answer to this crossword clue is the 6 letter word NODDER
I've seen this crossword clue in The Times
N
O
D
D
E
R
More clues leading to the result NODDER
Buddy explains!
The straight part
We know that "who offers a cursory greeting" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case who offers a cursory greeting = nodder.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.