A magnificent resource I have just stumbled on, in seeing if someone has already answered this question (do I look like a Turcologist to you?) is tourkika.com. An online Turkish grammar resource for Greek learners of the language, with lots of etymology for loan words into Greek.
The etymology… is enlightening.
Χαβαλές – havale. From Arabic حوالة (ḥawāla), meaning “transfer”. The phrase havale etmek in Turkish means to refer someone, to delegate someone to do something, to transfer responsibility to someone else.
What do Greeks do when they’ve been entrusted a task, and they’ve successfully delegated it to someone else?
They sit around a café, talk shit, play backgammon, crack jokes, have an ouzo.
Κάνουν χαβαλέ. “Doing havale”. Having fun.
EDIT: The related adverb χαβαλέ (Λεξικό της κοινής νεοελληνικής) means “doing something without serious effort”: Δε διάβασα· έδωσα εξετάσεις χαβαλέ “I didn’t study; I sat the exams havale”. Meaning “as if I delegated it to someone else, without taking responsibility for it”.