There's no guarantee you'll get anything if you do this. It's not enough to mark "damage" for the places I've worked for. You have to specifically say what is wrong, for example: "product received bent and scratched" and take photos. Never put 'box crushed' or 'box damaged', customer service will blow you off and you'll get nothing. If you get a shipment in a box that is crushed or ripped, make sure you open it and inspect the merchandise. If it's okay, go ahead and sign for it. If it's damaged I recommend you REFUSE it outright.
In the OP's case, he is unhappy with the product because of a slight or moderate manufacturing defect. In that case, some vendors will take the item back, some won't unless the damage is substantial. In this case the OP didn't post pics here so we don't have much to go on. I'm skeptical of such posts.