How to stop verification required when installing free apps
Sorry, but there is no way around that to download apps, even free ones. You will have to provide the App Store with a debit/credit card on file. Don't ask me why, I don't work for Apple.

If you don't want to use your real card, you can use an old card (even a prepaid one), even if there's nothing on it. You just can't purchase any paid apps and the card must not be past it's expiration

There's an official Apple support article on this, as found by IconDaemon.