When the Bride and Groom request no gifts, it’s really okay! It’s true that many people may give a gift anyway, but you should feel comfortable taking the couple at their word. And even if others do give a gift, you won’t look bad by comparison; after all, you’re only respecting their wishes.
For couples who don’t wish to receive wedding gifts, spread the message by word of mouth and on your wedding website. As wedding invitations shouldn’t have any reference to gifts, there’s no need to mention it there — in fact, you shouldn’t. Even though it might be seen as a “relief” to guests, it still distracts from the main focus of a wedding invitation, which is to invite those you love to share in your wedding.
If you do receive gifts despite your request, don’t make a fuss or refuse to accept them. A gentle, “You shouldn’t have!” wouldn’t be remiss, but don’t express annoyance or anger at having your request ignored. Thank the giver as graciously as you would for any other gift with a handwritten thank-you note sent within three months of returning from your honeymoon.