The district pays for their salaries and benefits.
They may or may not pay a finders fee which I am told varies between 2,500 to 5000 dollars. Sometimes it is paid for by government grants or through private donations but somebody is paying it.
TFA teachers also can get 5,500 a year for two tears (11,000 total) in loan forgiveness or in money for grad school, money that teachers who come from a more traditional route are not eligible for (and how is that fair).
Then there is professional development which can be expensive and since TFA teachers constantly leave it exasperates the need for professional development.
Imagine if we could spend that money on people who wanted to make education a career instead of short timers looking to fill lines on a resume or to do something until grad school starts.
Teach for America is not cheap. It's a bad deal all around.