Looking through some Jerome Gambit games from 2016, I noticed some "declined" versions.
On one hand, I can understand Black not wanting to give White the kind of game that the attacker wants.
On the other hand, as we have seen many times before, in declining the gambit piece(s) Black is exchanging an "objectively" won game for one where he is worse, if not losing.
In the following game, shugart at FICS, makes quick work of the situation.
shugart - amama
blitz 3 0, FICS, 2016
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+
4...Kf8 5.Bb3
White proceeds to play simple moves and out-play his opponent. He needed to face a greater challenge than that.
5...Qf6 6.O-O d6 7.h3 Nge7 8.Nc3 Be6 9.Nd5 Nxd5 10.exd5 Na5 11.dxe6 Nxb3 12.axb3 Qxe6
In typical defense-against-the-Jerome-Gambit-style, Black has returned the sacrificed piece - or, he would have, had he accepted a piece in the first place. Instead, unfortunately, he is now just down a Knight.
13.d3 h6 14.Be3 b6 15.Bxc5 bxc5 16.Qd2 Kf7 17.Ra6 Rhf8 18.Rfa1 Kg8 19.Rxa7 Rxa7 20.Rxa7 Rc8 21.Qa5 Qe7 22.Qa6 Kh7
A final slip, possibly in time pressure.
23.Qxc8
Black resigned
Here we finish up burying the 3...h6 and 4...Na5 defense to the Jerome Gambit by taking a look at 4.Nc3 - instead of 4.0-0 ("Too Much of A Bad Thing") or 4.c3 ("Still A Mess").
freerunner - gGgeorgGg
blitz, FICS, 2013
1.e4 e5 2.Nf3 Nc6 3.Bc4 h6
The Semi-Italian Opening.
4.Nc3 Na5
While the Semi-Italian Opening is playable for Black, and the Semi-Italian Jerome Gambit (4...Bc5 5.Bxf7+) has its risks, the introduction of ...Na5 pushes the whole defense over the cliff.
5.Bxf7+ Kxf7 6.Nxe5+ Ke8
6...Ke6 would get the same response.
7.Qh5+ Ke7
Or 7...g6 8.Qxg6+ Ke7 9.Nd5#, GriffySr - mackadee, standard, FICS, 2002.
8.Ng6+ Kd6
Let's face it, Black's King is already toast:
8...Kf7 9.Nxh8+ Ke6 (9...Ke7 10.Qxa5 Nf6 11.Qe5# shipwrecked - LScope, blitz, FICS 2011) 10.Qf7+ Kd6 11.Qd5+ Ke7 12.Qe5#; or
8...Ke8 9.Nxh8+ g6 10.Qxg6+ Ke7 11.Nd5#; or
8...Ke6 9.Qf5+ Kd6 10.Qd5#; or
8...Kf6 9.Qf5# moskvabr - amama, blitz, FICS, 2005.
9.Nxh8
This wins, as does 9.Qd5#, JakartaGuy - Kiloz, blitz, FICS, 2007 and (to use White's Knight) 9.Nb5+ Kc6 10.Nd4+ Kb6 11.Qb5#.
9...Nf6
Or 9...Qe7 10.Ng6 Qe6 11.Nxf8 Black resigned, xerthil - Tiur, blitz, FICS, 2005.
10.Qxa5
Picking up material while deleting a defender. Houdini gives a fun line using White's Queen Knight: 10.Nb5+ Kc6 11.Nd4+ Kd6 12.Nf7+ Ke7 13.Nf5+ Ke6 14.Nxd8+ Ke5 15.d4+ Kxe4 16.Qf3 checkmate
10...Qe7
11.e5+
Again, a line that shows the advantage of White's Knight being in play is 11.Nb5+ Ke6 12.Nd4+ Kd6 13.Nf5+ winning Black's Queen.
11...Qxe5+ 12.Qxe5+ Kxe5 13.Ng6+ Ke6 14.Nxf8+ Kf7 15.Nxd7 Bxd7
White has deftly exchanged a handful of pieces, leaving him simply a Rook and two pawns up. The rest of the game does not change this.
16.0-0 Re8 17.d3 g5 18.Be3 Bc6 19.Bxa7 h5 20.Bd4 Ng4 21.f3 Ne3 22.Bxe3 Rxe3 23.Rae1 Rxe1 24.Rxe1 b5 25.Ne4 Kg6 26.g3 Bd7 27.Nc5 Bc8 28.Re5 c6 29.b3 g4 30.f4 b4 31.Re4 Bf5 32.Rxb4 h4 33.Ne4 h3 34.Rb6 Bd7 35.Nc5
Fighting to the end, Black forfeited on time