The statement mentions the product containing ads and sharing information with ad networks. Nowhere else do I see anything about that on your web site.
You also want to use the addresses later on, not just to send one free card. Customers should know that.
"We use information held about you in the following ways: […] to provide you with information, products or services that you request from us or which we feel may interest you, where you have consented to be contacted for such purposes"
And if I don't give out the address for the person I'd like you to send a card to, you'll make him sign up too:
"We will mail your card as soon as your friend updates their address information at Bfore."
So, thanks for the offer but I'll pass.