2002 Honda Civic 02 Civic LX making a "woodpecker"

I can't believe the Dealer results ! Anyway, ck. Your outer axle boots to see if ripped. There will be grease on lower control arms, maybe even on inside of frt. Wheels. Even if they are not ripped, sounds to me like your outer axle joints are bad, especially when you say it's worse on turns. From a stopped posistion, turn steer wheel all the way to left. Take off & see what it sounds like then. Turn all the way to right & do the same thing. An empty parking lot works good for this procedeure if you have nowhere else. If it's more audible doing this, I'm certain it's the axle joints. If you return to Dealer, ask them to show you what they find. You have a right to ask & ask service manager to accompany you out to shop to look at your car on hoist. Did they even road test your car? Please let us know how you make out, or if we can assist you further. I worked on Honda cars for 18 years. You can even request to ride w/tech. Or service manager to point out the noise. Always ask for old parts, if they have to return core, you still have the right to see the old parts & get an explanation before they send cores back. Good Luck.