The authors agree that this surname is of Sicilian origin and has a dialect root. V. Blunda specifies that it comes from the dialect word grèstu, meaning "wild, of the countryside, rustic", an adjective that set the rural world against the urban one and was applied both to a place and to a person's character. As a surname, it could have originated in a nickname referring to someone of rough manners or to a peasant from the hills.

E. Rossoni places its presence in the Catania area, with cores in Paternò, Fiumefreddo di Sicilia and the city of Catania itself. The variant Li Gresti is described by Rossoni as absolutely rare and apparently linked to Paternò.