First of all there is no reading rainbow with LeVar Burton.. He is being sued for continuing to use the show’s catchphrase on his podcast, LeVar Burton Reads.
According to Refinery29.com:
Court papers reveal that WNED purchased the license for Reading Rainbow’s intellectual property, including Burton’s tagline, “But you don’t have to take my word for it.” The deal allowed RRKidz, the show’s production agency, to handle digital distribution of the show while WNED focused on actually making new episodes. Burton came in later, with his Kickstarter campaign — and its $6.5 million raised — and hopes to revive the show. According to WNED, that was a breach of contract, since the broadcaster saw the move as an instance of forgoing creative control.
The network claims that the slogan will always be associated with Reading Rainbow and Burton’s continued use of “but you don’t have to take my word for it” will confuse and deceive audiences into thinking that they’re listening to official Reading Rainbow content. WNED is looking to keep Burton from using the phrase in future episodes of his podcast and for a share of his profits.