I got Swain.
They will not replace it. It is, after all, a mystery. If you could just say "Nah, I want something else" it would defeat the point. If you want a specific champion, you buy that champion. Mystery gifts are a gamble by their very nature.
Also, give Swain a chance. He takes a lot of getting used to, but Jericho Swain is one of the most badass people in the League.
You're stuck with it. THey won't remove it, they won't give a different skin.
Sadly Riot won't remove champs from your account. If they would, I wouldn't have Teemo.
Edit: If they actually said that 'if you don't want this c hamp' line, then this may be an exception. I didn't see that line, so it might be worth your time to ticket it.
Nono Guys, Downvote it, that'll get it answered. Thanks :)
I got swain too. I'm just glad I got a champion of high I.P. value, instead of like, Teemo, or Nasus.
Let us know if it's actually possible :P
I saw someone at Riot say they'd be happy to remove the champ if you send in the support ticket, but you won't get a replacement.
Meh.. I'm in a similar situation.
But it's a random gift, it would really beat the purpose of itself if we could just "reroll" it.
Here's the official message from Riot.
If you received a champion you do not want, you can submit a ticket to have it removed from your account. This will not result in an exchange, or alternative compensation, but we can remove any content you wish off your account.
most likely remove it you probably wont get a new champion
Swain is the best. 
Bird is the word
