DRYDEN, N.Y. — Four years ago a man and a woman knocked on Katharine D. Dewart’s door, offering easy money for the use of her land.

Handing her a brochure that included serene before-and-after pictures, they explained that a natural gas company was seeking to drill somewhere on her 35 acres of wildflower fields surrounded by hemlock woods in this Tompkins County town near Ithaca.

Ms. Dewart, 68, served lemonade and signed, accepting $1,909 upfront and royalty payments of 12.5 percent of any sales of gas extracted from her property. “I assumed it’d be noisy for a couple of months, and I’d have a little extra cash and wouldn’t that be great,” Ms. Dewart, a writer, said.

Now, she said, she is stricken with remorse. And she is not alone. Hundreds of other state residents who signed leases allowing gas companies to drill deep into their properties with a method known as horizontal hydraulic fracturing have changed their minds and are trying to break or renegotiate their contracts. Millions of acres in upstate New York are under lease, awaiting permits for the drilling, which has yet to begin, delayed by a state environmental review.