The lawsuit, brought by Abby Grossberg, accused the cable network of pressuring her to lie in a deposition. Her lawyers say they intend to refile the case in a different jurisdiction.
Private messages sent by Tucker Carlson that had been redacted in legal filings showed him making highly offensive remarks that went beyond the comments of his prime-time show.
The two hosts took very different approaches, but the decisions by Fox News and CNN to shed the stars marks at least a temporary shift in the excesses of Trump-era coverage.