Cr Hilary Calvert said in a letter to the editor her husband had withdrawn his objection.
His objection concerned a "debate about how the city applies its rules throughout Dunedin which does not need to be dealt with in the context of the application made by Vogel St Kitchen'', she said in the letter.
Mr Broad declined to respond to questions from the Otago Daily Times, saying: "I've got nothing more to say than what's in the letter.''
However, he failed to understand why the objection was made in the first place, saying he could not think of a "rational reason'' why he did it.
He was pleased Cr Calvert said in the letter she was "on the same page'' when it came to the value of the warehouse precinct.