National Rifle Association CEO Wayne LaPierre charged the organization’s ad agency more than $240,000 for expenses related to trips he took to Italy, Hungary, the Bahamas and other locales without providing adequate documentation, according to a letter from the ad agency given to the group’s board last week and described by people familiar with the matter.

Some of Mr. LaPierre’s expenses were charged to one of the ad firm’s credit cards, the people said, and overall costs included a 2014 stay at the Four Seasons hotel in Budapest and expenses related to trips to Palm Beach, Fla., and Reno, Nev. The ad firm, Ackerman McQueen Inc., was reimbursed over time by the gun-rights group, these people said.

The disclosure of the travel expenses came to light because of an extraordinary falling-out between the NRA and Ackerman McQueen. The previously unreported letter, dated April 22, played a role in the recent turmoil inside the NRA, and raises new questions about whether Mr. LaPierre benefited from dealings with NRA vendors.

An outside attorney for the NRA, William A. Brewer III, said the “vast majority of travel involved donor outreach, fundraising and stakeholder engagement. The board is aware of the allegations and has taken them under review.”

Mr. Brewer said certain fundraising and travel expenses were routed through Ackerman McQueen for “confidentiality and security purposes,” but the practice has since been modified. Mr. LaPierre didn’t return messages left at the NRA.