Jerome Gambit: Out-Stranged?

One of my games in the "The Italian Game" tournament at Chess.com has started 1.e4 e5 2.Nf3 Nc6 3.Bc4 g5!?

Wow.

I guess that's one way to avoid the Jerome Gambit - 3...Bc5 4.Bxf7+.

I have never seen that move before.

Since it is similar to the Brentano Defense to the Ruy Lopez - 1.e4 e5 2.Nf3 Nc6 3.Bb5 g5!? - (Franz Brentano, "Neue Vertheidigung der spanischen Partie", Wiener Schachzeitung, April-May 1900; February 1901; and January 1903) I am inclined to call it "the Brentano Defense to the Giuoco Piano", except that the earliest game example that I have found is from a game played in Detroit in 1990.

Needless to say, it was not played by Franz Brentano (1838–1917).

As always, more research is needed.