How do I delete podcast episodes "Synced from iTunes" in iOS 13?
Here's the workaround I found - on your iPhone, launch Podcasts, select a program/show, go into Synced from iTunes and tap the plus button on each episode and then tap the download button.

Once the download completes for all the episodes, Synced from iTunes will disappear.

This workaround was based on an Apple Communities post I saw. 

I also have a post about this on my website if you are interested.