Diccionario Castellano, 1787: in Malaga, "foreigners who have a certain type of accent which keeps them from speaking Spanish easily and naturally" were referred to as gringos, and the same term was used in Madrid, particularly for the Irish. Gringo
The term is therefore 60 or more years older than the Mexican War. The origin in this write-up is "most likely that it came from griego, the Spanish word for Greek." The word could have been introduced into English through the Mexican-American War.