Gayle King got set up to look like an insensitive troll because her network posted a salacious promo ... that's how some staffers at "CBS This Morning" feel anyway.
Sources connected to the show tell TMZ ... some of Gayle's coworkers are incensed over the backlash she's getting because a promo clip of her interview with Lisa Leslie about Kobe Bryant, included a question about his 2003 sexual assault case. Lisa pushed back, making it clear ... in her book, it's not relevant to Kobe's legacy.