What is Thanks, But No Thanks?
1.
a way of saying a polite no!
Thanks can be used to show approval. It could also be used to avoid doing sth undesirable and hence a No-Thanks.
Smith: How would you like to hang out with Lisa and Jane.
You: Thanks, but no thanks. I hate that fat chicks man!
See
2.
When you want to emphasize something wonderful you did, that you didn't really do.
Sarah Palin:
I told congress about that bridge to no where, "Thanks, but no thanks!" Then I took the money.
you: Wow, good job, Sarah