Normally, I just take the pawn, develop normally and give the pawn back.
White's wasting a a bunch of moves to trade pawns rather than just taking with their pawn and gaining tempo on your Queen as per standard. I don't think you can be in too much trouble, and you can keep your pawn structure more or less the way you're used to it being in the Scandinavian.
The Tennison Gambit is a complete and utter joke!
1.Nf3 d5 2.e4 (or 1.e4 d5 2.Nf3, but I would never reach it myself via this move order) 2.dxe4! 3.Ng5 e5! 4.Nxe4 f5! 5.Ng3 Bc5! with a significant advantage for Black!
5... Ke6?? is a joke. Simply 5... g6 6. Bc4+ Kg7 7. Qxe5 Nf6 and White is busted.
6... Nf6 or 8... Nf6. White is still busted.
I'm absolutely convinced that 4. Nxf7 is a joke. There is very little that justifies the sacrifice.
Post number 10 is a total joke! He gives absolutely no explanation or justification for his choice of moves for Black, and merely wants to play what works for White, and even in the final position, Black's winning! Therefore, back at him, no justification for White's moves below, but there is no need for justification - other moves make Black's win even easier!
1...Qxa7 2. Bxa7 Ra8 3. Bd4 Rg8 4. Nc3 Kf7 5. a4 Rgd8 6. Nb5 Be7 7. Bc3 Bd7 8. Nc7 Rab8 9. O-O Bc6 10. h3 Rdc8 11. Nb5 Bxb5 12. axb5 Rxb5 13. Re1 Ra8 14. Rxe4 Ra2 15. Rf4+ Ke8 -+
3...Bf5, and white is a tempo up in a reversed Budapest.
A "ltttle" detail: the extra tempo (the pawn is on c7, not c5) is very advantageous to Black.
Anyway, 3...e5 cannot be bad, either, and certainly 4.Nxf7? is less than a joke: 4...Kxf7 5.Qh5+ g6 6.Qxe5 Nf6 (why Black should block the most convenient square for his king with 6...Bg7?) and white should already pack and go home.
Tennison himself is a very interesting character, He was in love with a lady from the South who refused to marry a Yankee soldier. He absconded to be with her. He was chased, almost caught and when he arrived in the South almost hung as a spy.
so what does stockfish say about the analyses by some forgotten correspondence master?
It says Tennison is just busted and the lines given below as good for black are really good while the lines given by die hard tennison fans are just bad...
And there is no "horizon effect", at least for white's compensations. The more the engine "thinks", the more black's advantage grows up.
I could only find one game featuring the stupid move 4.Nxf7?- regular OTB, pre-computer era. It lasted some eight moves too long:
Needless to say that 4.d3 is much better, when white is "just" somewhat worse.
I know. Stockfish is the end of chess. Morphy would not be able to win against stockfish, neither would be Tal.
Only brute calculation. No more romantic games, no more imagination,bluff, fantasy.
Its just the end of chess.
Its no more a game, just as the war, no more strategy, the guy with the most bombs will win.
Shame on you all, you dont realize the beauty of human chess.
I think I speak for everyone here when I say we very much do. Human chess is about making the best moves you can. It’s playing for tricks that is antithetical to human chess. I believe that in the end, chess is a fair, objective game, which means that you cannot succeed in doing anything if the position does not merit it.
I could only find one game featuring the stupid move 4.Nxf7?- regular OTB, pre-computer era. It lasted some eight moves too long:
Needless to say that 4.d3 is much better, when white is "just" somewhat worse.
Exactly, and because I’m a boring player who doesn’t believe in letting gambiteers have any fun at all, I then play 4... Be7! 5. Nxe4 f5 when the position is pleasantly normal and also pleasantly better for Black.
I'm absolutely convinced that 4. Nxf7 is a joke. There is very little that justifies the sacrifice.
I agree. I've calculated all the lines, and I don't see anything for white.
The tennison-gambit is a good way to surprise scandinavian players because they have to switch-off their auto-pilot and usw their brains.
The best way to surprise opponent is to play good chess.
Tennison Gambit could be deadly in bullet, no time to think and could easily make a mistake and lose. 
What should be black's next move?