what does "none taken"here mean?
“He doesn’t have time to waste on underlings. He’s too important. I get him.”
“Yeah, he made that clear,” Mike agreed. “So, he comes in later that week. Expensive suit, two-hundred-dollar haircut. He’s got that enti-tled, prep-school superiority all over him. No offense, you probably went to one.”
“I did, and none taken. I know the type.”

Question

what does "none taken"here mean?
“He doesn’t have time to waste on underlings. He’s too important. I get him.” 
“Yeah, he made that clear,” Mike agreed. “So, he comes in later that week. Expensive suit, two-hundred-dollar haircut. He’s got that enti-tled, prep-school superiority all over him. No offense, you probably went to one.” 
“I did, and none taken. I know the type.”

Answer

"None taken" is in response to the comment "no offence". Sometimes you might hear "no offence intended" too.

Or in other words:

"No offense": "I don't mean to offend you" or "I don't mean to upset you deliberately" 
"None taken": "No offence taken" or "I didn't take offence" or "You didn't upset me."

The first speaker described a stereotype before he realised his companion could fit the same description, so he said "no offence" as soon as he realised to not cause upset.

Hope that helps!