As far as I know, you don't. I personally do not play video games, but have auctioned off a few of these and no one has ever commented that you need one. Below I have pasted the code redemption instructions that came with the card and it does not mention having to have a credit card. Hope that helps! :)
1. Log in to your Xbox Live account on www.xbox.com/redeemcode. Note: If you do not have an Xbox Live account, you will need to create one (or you may log in with your Microsoft account). Create a new account at www.xbox.com/redeemcode by clicking the sign-up link in the message at the bottom of the page: “Don't have a Microsoft account? Sign up now”. Alternately, create a new account at https://live.xbox.com/en-US/Home.
2. Once logged in to www.xbox.com/redeemcode, click “Redeem”, enter your 25-digit code (above), and click “Confirm”.
3. If you require further information on how to redeem codes on your Xbox 360 and Xbox One, visit www.xbox.com/howtoredeem-console.