If you mentioned the wrong school, this is an automatic ding. Every school says this in their brochure. Standard policy.
Obviously that's not good, but there's nothing you can do about it now. It really just depends on the interviewer, and if he/she will care. In general, a thank you note is a good idea, but probably doesn't "officially" affect your application. It's more of a "right thing to do" kind of thing.
Be careful about bringing too much attention to this mistake. Sending an official letter to the admissions committee will just draw their attention to it and make things worse.
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