Removing Podcasts Documents and Data
A forum post on Apple Support Communities points out that on iOS 10 it is possible to reduce the Podcasts app’s “Documents &amp; Data” by temporarily removing the app:


  Good news for everyone that has been dealing with this issue - iOS 10 has a new feature that help resolve the Podcasts storage problem.
  
  One thing you can now do in iOS 10 is 'delete' stock apps from your device. It doesn't really delete the app, but it deletes the icon link from the apps and it also removes associated data and configuration files!  This means that deleting the Podcasts app will also delete the huge data file.
  
  Once removed, the Podcasts app can just be readded from the App Store, and the settings are instantly restored from your iCloud account.
  
    


( I realize this is an old question, but I stumbled upon it while trying to find out why the Podcasts app is using a few hundred megabytes worth of “Documents &amp; Data” on my iPhone in addition to the storage it uses for downloaded podcast episodes, and I thought it was still worth providing an updated answer pointing out that on iOS 10 this can be more easily fixed. I haven’t been able to try this myself yet, as I am still on iOS 9. )

ONE THING TO NOTE:
Any podcasts you have downloaded, but are not subscribed to will be lost.