Most boxes and bundles are wrapped in mylar, which does not pass water vapor (cellophane does). For one reason and another, I've had mylared boxes and bundles sitting out for a month or more before I cut into them, without apparent loss of moisture let alone damage to the sticks.
I've also had, through the same UPS routes (six-seven days from there to here, soggy or dry), a few bundles that were so dry I didn't dare remove the sticks from the bundles once I'd noticed a foot crack or two.
If you get dry cigars, it's almost certain they got dried out in the vendor's warehouse, not in shipping. This is a bit more common among "closeout specials" that try to get warehouse room for brands that move, or for this season's shipments of The Regular Stuff -- both scenarios have cigars in the warehouse "too long" and not among the regularly-inspected and rotated stocks.
As long as the wrapper isn't actually cracked or peeling, just put the whole slit -- but not fully unwrapped, the less handling, the better -- bundle in a humidor at ~70% RH for a week or two. The wrappers will absorb moisture first, softening and swelling ahead of the filler, so you can even rescue a bundle that already shows some damage, provided you do not handle the individual cigars, and the bundle as little as possible.
Returns/complaints are entirely up to you, but I'm not talking about a $500 box of Graycliffs, here, and such stuff would never ship in that condition, anyway.
Me: The price is not worth my repacking and sendoff, I HATE the phone (coming or going), robot e-mail responders almost as much, and, hey, if it ain't too broke I can fix it myself.
I pay overall attention to quality and service from distributors and brands, and general competition does far more to fix the baddies than I can by listening to 40 minutes of Muzak and robot ads over an 800 number.
Guluk, and VELcome to se CAStle.