Green’s Dictionary of Slang

grego n.

[SE grego, a coarse jacket with a hood, worn in the Levant, ult. Lat. Graecus, Greek]

a rough greatcoat, with a hood.

[UK]J. Davis Post Captain (1813) 2: Mr hurricane [...] threw off his grego, that is, his great coat.
[UK]C.M. Westmacott Eng. Spy II 175: A good grego in a winter’s watch.
[US]Melville Moby Dick (1907) 25: Going to his heavy grego, or wrapall, or dreadnought, which he had previously hung on a chair, he fumbled in the pockets.