If I'm going to hammer something I usually go out and do it on the garage floor, just to be sure. Supposedly you can use the little mat that comes with the texture hammer, but I don't trust that or my table and just feel better doing it out on the cement.
The 'block' that came with the Texture Hammer feels like a piece of laminated cardboard. I really don't know what real purpose it has...
But I love the texture hammer!
I bought some sets of metal stamps- and I had to use them to stamp the metal blanks ONLY on a really hard surface. It cannot have any give, whatsoever. I bought a steel block (that was next to the metal stamps at HL) and that's worked best for me. Second best was a huge solid wood cutting board that was in the kitchen. And I ruined it. So I recommend getting a steel block, if you're serious about stamping lots of metal, or something similar.
Since you're using steel stamps, you could possibly use the rubber or the metal head of the TH hammer. I don't have it so I don't know how much weight the hammer has or how soft the heads actually are. The act of hitting the steel stamps may damage your heads. Or, if the TH hammer head is hardened steel, hitting a stamp with it could be dangerous because of bounce-back.
Also, it looks like a small, lightweight hammer? Depending on the thickness and type of the material you want to stamp you may have to throw a fair amount of heft into your swing to get a good stamp impression. For a good impression you want to hit your stamp only once. No tapping or multiple hits, you're likely to get a blurred image that way.
Regardless, a steel bench block on a stable surface would be the the best thing to use as an anvil. The garage floor or the sidewalk would also work, but the cement would likely texture the back of your material (which may look good! you'd have to decide).
And of course, always do practice pieces first. Stamping 20 gauge metal requires different finesse than 10 gauge. And stamping copper is different than stamping 14K gold. So, test pieces!
I have just started using the metal stamps myself. I have a bitsy anvil, but don't really like it. I think I will look at HL for a bigger steel block. Thanks for the suggestion Corey! Best wishes with your stamping Scrappy day!