STAMFORD, Conn. — When Lexene Charles got into his car here on the Saturday before Martin Luther King’s Birthday, he was stunned by what he saw outside his home. He called for his longtime partner, Heather Lindsay, to come outside.

Someone had spray-painted an anti-black slur across it, Mr. Charles, who is black, said. But instead of scrubbing it off, he and Ms. Lindsay, who is white, decided to leave it up to make a very public point about intolerance.

Six weeks later, the graffiti, which faces High Clear Drive, remains. Residents have started to complain, and officials in Stamford, a diverse coastal city about 30 miles northeast of New York City, recently directed the couple to remove it. Leaving it up only brings satisfaction to the vandal, the city said.

On Feb. 7, after the slur had been up three weeks, the city issued the couple a citation for blight and a warning: Remove it, or face a $100-a-day fine. The police chief visited the home and offered to clean the garage door. The mayor said he would help. The couple refused their offers and ignored the citation.