You have a video that was imported from Youtube, but you don't want it on your site. You delete it, and the next day the video has re-appeared on your site. How do you delete the video so it doesn't come back?

You can delete videos in podcast by going to Design > Youtube Importing

Edit the Video Post (Pencil on the Right) and scroll down and click on Delete at the bottom. This only works temporarily.

Podpage can import your entire channel (ALL VIDEOS). It checks your YouTube Channel on a regular basis and imports any new videos.

If you edit the video post in Podpage and remove it, it will reappear.

Instead of importing your channel and all of the videos on YouTube, you can import a playlist from your YouTube channel instead.

Then if you want a video to be embedded on your Podpage site, you simply add that video to the playlist you are using as the source for the import.

EXAMPLE:
You could make a playlist in YouTube named, "For Website." Then use that playlist when you set up Podpage to import videos.

Now going forward, any video added to that playlist will imported into Podpage.
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For more information see this tutorial from YouTube.