Gringo has been defined in another thread (too muck work to check back so here is the word again).

Gringo was applied by Spaniards to foreigners, especially French, in the 18th century. Origin of word unknown, but may have first meant "unintelligible gibberish," one of its definitions in Spanish Dictionaries (Diccionario de la lengua Española, Real Academia Española).

Through much of Latin America, the word has been applied to foreigners (extranjeros), especially those speaking English. In Mexico, applied to North Americans. Hablar en gringomeans to speak double Dutch. (Velasquez, Spanish and English Dictionary).
"gringada" is applied to females.

A participant in the Mexican War heard the word "gringos" hurled at them by Mexicans in 1849 (See Oxford English Dictionary.

The "laurel" song does not appear in any American writings before the 1860s, and was apparently unknown to Americans during the Mexican War.