An Iowa woman allegedly demanded that Discovery Communications cancel the TLC show 19 Kids and Counting or pay her $10,000 -- otherwise she would release compromising photos of 25-year-old Amy Duggar, Jim Bob Duggar's niece.

Teresa Hunt is facing federal charges after being arrested for threatening the TLC parent company and the Duggar family.

According to an affidavit, Hunt sent Discovery Communications a letter providing details of Amy Duggar's alleged affair with a much older musician.  Hunt reportedly tried to sell photographic evidence of said affair to RadarOnline.com -- who described the photos as merely harmless snaps rather than incriminating, damning photos.

RadarOnline did not purchase the photos and claimed to have no knowledge at the time of the extortion plot.

19 Kids and Counting follows the life of Michelle and Jim Bob Duggar, a deeply religious couple who have 19 children. According to RadarOnline, Hunt is quoted in the affidavit as accusing the Duggars of popping out babies to keep their ratings up.

Amy Duggar denied the affair in a statement to RadarOnline.

It's totally untrue, Duggar reportedly said. He is a longtime family friend who has always been supportive of my music career. He's a good Christian and it's upsetting that his generosity has been exploited like this.