I just went through this issue. In fact still am going through it. I'm on a merged server and tried redeeming some TCG pets. Landro said he couldn't validate the codes. I've copy and pasted, deleted wtf, cache, and interface folders. Nothing. Started a goblin on an unmerged realm (mainly to get the Shore Crawler) but that didn't work either. After a few tickets, I find out that this is a known issue with realm connections.
You should send in a ticket with both the code from the card and the code received from the redemption website. They will do something on their end and in a few weeks you should be good to go.
I've gotten codes back from my ticket, but they still didn't work. Turns out that Blizzard actually messed up and sent the wrong thing back so now I have to wait another week or two. One plus is supposedly they will redeem them themselves and put in my inventory. So I don't have to mess with it again. Fingers crossed.