I have said this before, many times: It is not enough to know that the Jerome Gambit is refuted; it is not enough to know the move that refutes it; it is not enough to play the refutation - as Black, you have to win the game.
It is helpful for the defender to know that out of 12,686 games in The Database that start 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+, White wins only 45%. The following game, however, is one of those times.
Wall, Bill - Guest7715764
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+
4...Kxf7 5.Nxe5+ Nxe5 6.d4 Qh4
This is probably the strongest response to 6.d4, although you wouldn't know it by Bill's record against it: 13 - 0 - 1.
This is one of a number of continuations for Black, here focusing on development rather than saving a piece - one has to go, anyhow.
8.dxc5 Qxe4 9.Nc3 Qb4
You may ask yourself, "What does White have here?" Good question. The game will be over in a dozen moves, so watch closely.
10.Nd5 Qxc5 11.Nxf6 Kxf6 12.Be3 Qc6
This seems simple enough, but it allows White to win back his sacrificed piece and achieve an even game.
Remember the old adage: When White has equalized in the Jerome Gambit, he has the advantage.
13.Bd4 Rf8 14.f4 Kg6 15.Bxe5
Who is better now? Look at Black's d-pawn blocking his light-squared Bishop which is blocking his Rook... While Black works on this situation, his King falls deeper into danger.
15...d6 16.Qd3+ Bf5 17.Qg3+ Kf7 18.Qxg7+ Ke8 19.Rfe1
19...dxe5 20.Rxe5+ Be6 21.Rae1 Black resigned