“It couldn’t be a clearer-cut case, actually,” said Clive Cheesman, one of the college’s heralds, who oversee coats of arms, their design and their use.

“A coat of arms that was originally granted to Joseph Edward Davies in 1939 by the English heraldic authority ended up being used 10 or 15 years ago by the Trump Organization as part of its branding for its golf clubs,” said Mr. Cheesman, a lawyer by training. “This got them into difficulty.”

The White House referred questions to the Trump Organization, which did not respond to requests for comment.

Image Mr. Tydings wears a ring with his family’s coat of arms. Credit... Jared Soares for The New York Times

The organization has trademarked the Davies coat of arms in the United States, which has far less attachment to such symbols. It is used on the company’s website and is a prominent branding detail of Mr. Trump’s many American golf courses and resorts — emblazoned on golf balls, shirts and bottles of body lotion.

When the Trump Organization created a Civil War memorial at the golf course near Washington commemorating a battle and a “river of blood” that never occurred, a plaque marking the fictitious event was embossed with the coat of arms.

Mr. Tydings, 89, was close to Ms. Post, his step-grandmother, whom he referred to as “Mommy-da.” He spent much of his youth at Mar-a-Lago. His grandfather, Mr. Davies, was a lawyer and diplomat, also serving as ambassador to Belgium and as a special envoy for President Harry S. Truman.