How do I delete a downloaded podcast episode?

If you'd like to delete an episode while online: 

Go to your Library and tap on the "Downloads" button > Select the "Three dot button" next to the podcast you'd like to delete and the delete option will be available.

If you'd like to delete an episode while offline: 

Go to your Library, and tap on the downloaded episode you’d like to delete. From there, you’ll be taken to the offline version of the podcast profile, which will display all of the episodes you downloaded for that particular podcast. Tap the three-dot menu button on the episode you’d like to delete, and a menu will appear with the option to delete it."