The coat of arms was patented and granted by the Queen’s father George VI in 1939.
It features the words “Cadernid Cyfiawnder Cynnydd” – Welsh for “Stability Justice Progress” – under two unicorns, a boat and the Welsh dragon.
Barry councillors had threatened to take Mr Martin to the Court of Chivalry, which was set up in the 14th century but has not sat since 1954.
Mr Martin called the row “extreme”, adding: “I think it’s a question of trying to balance the strong feeling of our customers who overwhelmingly say we should keep the carpet.”