Am I being environmentally irresponsible by purchasing teakwood items?

No. Eventhough Teak is a precious resource across the globe and currently there are only four countries in the world that contain natural teak forests; Burma, Laos, India, and Thailand, with Burma (Myanmar) account for approximately 80% of the world's exported natural teak supply, there are now companies transplanting seeds from Burma into South America and Africa, hoping to farm teakwood more responsibly by utilizing eco-friendly logging techniques (immediate replanting). Teak forests are now also highly regulated due to increased demand, ecological and economical impact, and often sub-standard working conditions on plantations.

By purchasing antique teak items you are essentially recycling this precious wood  - which is a very environmentally sound practice!