I recently reset my iPhone and restored it using my latest iCloud backup. I noticed in the podcast app that four Christian podcasts appeared under a "Not Subscribed" section (seemed interesting that all of the podcasts had the same general theme). I had never subscribed to, or even heard of, the four podcasts. I deleted them and closed the podcast app. Now each time I reopen the podcast app, one of the podcasts continues to reappear and attempts to start downloading an episode.
I found this question that sounded oddly similar, but it had no answers.
I tried removing all podcasts and syncing with iTunes on my computer (which shows no current podcast subscriptions), but this random podcast still appears.