If you add activated carbon to the filter it should get rid of the tannins. Also, water changes will dilute it, but the wood might keep leaching tannins.
Hello cp. Tannic acid can mess with the pH of your tank water. Your pieces appear fairly small, so by just removing and replacing the tank water a bit more often, I doubt your fish will notice any changes.
Nice looking tank! Your fish will probably appreciate some tannin in the water. Just keep an eye on the pH, as already advised, and use water changes and/or activated carbon to keep the brown to an aesthetically pleasing level.
The best way to remove tannins is with big water changes. Do a 75% water change a couple of times a week or whenever it looks too dark for you.
Make sure any new water is free of chlorine/ chloramine before it's added to the tank.