You have some options open to you that go beyond taking your feline to the animal shelter or rehoming her. First, learn just why all cats scratch. Second, learn to trim her claws -- it's not hard at all!
When you have your scratching surfaces ready to go, they need to be placed where they'll be used. Remember, clawing is in part a marking behavior for your cat, so it's likely she's returning to the same place to scratch.