New Orleans real-estate developer and entrepreneur Sidney Torres IV has won accolades for his success in cleaning up the French Quarter after Hurricane Katrina and for fighting crime in the storied historic district, sometimes spending his own money.

But the achievements have done little to damp the outrage some preservationists have expressed over Mr. Torres’s renovation of the 4,600-square-foot house and stable building he purchased in the district four years ago.

Some of the work didn’t get the proper permits from the city’s Vieux Carre Commission, which oversees the French Quarter, and preservationists say he should be forced to undo it.

Mr. Torres, a host of the new CNBC home improvement show “The Deed” and a possible candidate for New Orleans mayor this year, acknowledges mistakes were made by his contractor but says the house has remained well within the character of the neighborhood.

“These are things that would have been approved anyway,” he said in an interview.