Mr. Groves recalled, “I said, ‘If I’m going to be murdered, is it going to be by a criminal or a law-abiding citizen?’” The caller grumbled and hung up.

Mr. Groves said he grew up in a family that hunted and included members of the N.R.A. In recent years, though, he said the organization has become more focused on lobbying, gun sales and politicizing gun ownership in an attempt to frighten owners into thinking that other Americans want to take their guns away.

“That is simply not true,” he said. “This experience has hardened my position.”

Mr. Groves said he asked the public about what organizations should get the restaurant’s $15,000 check. Several people suggested Moms Demand Action, which was founded in 2012 by Shannon Watts, a former communications executive, in response to the shooting at Sandy Hook in Newtown, Conn., which left 20 schoolchildren and six adults dead. The grass-roots network has quickly grown into a leading force for gun violence prevention, with chapters in 50 states.

“Most Texans, including gun owners, agree that we’re all safer with some common sense gun laws in place,” said Donna Schmidt, a volunteer with the group’s Texas chapter. “The N.R.A.’s radical leaders oppose common sense, and we’re grateful to Ellen’s for standing with the rest of us. The ground is shifting, even here in Texas.”

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