The older operation cleaned something up; the familiar modern one muddles it.
The proposed deeper route includes Arabic ghirbāl, a sieve, and a verb of sifting. Middle English garbelen meant removing impurities from spices. Modern garble often makes a message less clear instead.
The Arabic route into French is probable, with possible Italian mediation. The selected forms and glosses are documented, but the puzzle does not make one complete borrowing chain certain.
Source
Merriam-Webster: garbleWord History supplies ghirbāl, sieve, as part of a qualified Arabic route, and explicitly glosses garbelen as removing spice impurities; modern definitions concern distortion.