Green’s Dictionary of Slang

(Aus.) a southern European immigrant, esp. a Greek.

1957		J.M. Hosking Aus. First and Last 123: We call them New Australians now; once we called some Dagoes, / Others Balts and Squareheads, Pongoes, Grills and Rice and Sagoes .
1967		‘Whisper All Aussie Dict.’ in Kings Cross Whisper (Sydney) xxxv 6/1: grills: Greeks. From the ability of industrious Greeks to control country town cafes.
1970		J.S. Gunn in Ramson Eng. Transported 53: Grill, ‘Southern European’ [AND].