A federal judge has dismissed a lawsuit that claimed a Florida landscape architect firm’s drawings led to the denial of a local couple’s plans to build their dream house on James Island, a wooded seven-acre peninsula in Cohasset’s Little Harbor.

John and Jane Steinmetz, both lawyers, have appealed US District Judge Denise Casper’s decision to the First Circuit Court of Appeals.

“I am extremely disappointed with the court’s ruling,’’ John Steinmetz said. Casper ruled on July 29 that the firm of Coyle & Caron was covered by the so-called anti-SLAPP law, which protects people participating in public affairs.

Casper also said that the firm’s drawings of the Steinmetzes’ proposed home did not directly cause the project to be rejected, as the couple alleged.

In their lawsuit, the Steinmetzes had argued that the Cohasset Conservation Commission voted against their plans in part because of drawings by Coyle & Caron that made the house look far more imposing and conspicuous than actually proposed. A neighborhood group called Save James Island commissioned the drawings.

The Steinmetzes, who live elsewhere in Cohasset, bought James Island for $1.2 million in 2014 and have been trying to build a 7,800-square-foot home on it. The Conservation Commission has twice rejected the plans on environmental grounds.

The Steinmetzes also have appealed to the state Department of Environmental Protection.

Johanna Seltz can be reached at seltzjohanna@gmail.com.