The fakelore which ties Gringo to Green Grow, or the Mexican War, or something Irish is one of the hardest bits of mis-information to kill among folkists.

The thread pointed out by Masato includes a posting of the word's occurrence in the "Diccionario Castellano" (1787)- "Foreigners who have a certain type of accent which keeps them from speaking easily and naturally." The word was also used in Latin America before the Mexican War (see other posts).
That the word was derived from griego seems likely.