Tannins are not harmful at all.... In fact, many say that they are healthy for fish. Simulates their environment better... It's just that you might not want your tank looking like iced tea.
If you didn't boil the driftwood already, take it our and do it now.
Reason 1: It sterilises the wood and prevents any nasties from entering the tank
Reason 2: It helps get the tannins out.
Water changes will remove the existing tannins.
If you don't remove the tannins now, your tank will look like tea for a while, possibly months. But again, its not dangerous at all. I boiled my driftwood for 2 hours and I still get a few tannins leeching into the water column.