On your site https://wordpress.com/home/{site}, where you’ve already gone through the introductory set-up tasks, dismiss the cards at the top until you see the podcast card.
Click on “Get Started”. This should take you to https://anchor.fm/. Clicking on “Hide this” should dismiss this card.
Screenshots and GIFs
Fixes 310-gh-dotcom-manage
Unfortunately, no screenshots were provided by the developer.