I think if you wash it in the sink that might take away the seasoning you've been giving it. A good scrub with a wire brush is all it needs, and oil before every use.
If you like to grill a lot then the drip tray becomes so important. I forgot to clean it, or at least I was procrastinating doing it, and the drippings caught fire and made a hell of a mess, coating my meat in a thick, dark smoke with a very sharp taste. It almost cost me the whole load of meat. Now I make sure I keep it clean.