Braun, meeting with reporters Wednesday for the first time since accepting a 65-game suspension in July, said he had not provided any financial compensation but said he and Laurenzi had "made amends."
"It was an incredible experience," Braun said. "It was extremely kind and gracious of them. They're really special people and I appreciate them giving me the opportunity to go to their house and have a conversation in person.
"I wish that I could change it. I wish that I hadn't said anything about him. I wish I knew more at the time I said what I said. But he was really a special person and his family was a special group of people."
Laurenzi collected the sample that triggered a positive test, but Braun won an appeal in 2012 and averted a suspension. He accepted the suspension this year based on evidence gathered in baseball's investigation into the now-closed Biogenesis clinic in Florida.
Braun repeatedly declined to provide details in his answers, according to this transcript from the Milwaukee Journal Sentinel. He said he wrote a letter to Commissioner Bud Selig but did not elaborate. He declined to discuss whether his suspension should invalidate his 2011 National League most valuable player award, when the Dodgers' Matt Kemp finished second in the balloting.
Braun did say he saw no reason his performance should decline next season.
"I think I will be better," he said.
He also said the suspension and fallout has strengthened his relationships with his fiancee and family.
"Dealing with the wedding," he said, "has been far more stressful than this situation."