How do I delete a podcast from iTunes 12?

I have a couple dozen duplicate Podcasts in my iTunes library, and I'd like to delete them.

Here's how I think it's supposed to work. Right click, then click "Delete". In fact, that does work sometimes. Check here:

However, I don't wish to delete that Podcast, so having the option doesn't help. If, however, I try the same thing with the next item down…

… there are fewer options, and "Delete" is not among them.

BTW, if I click "Play" the podcast plays.

If I click "Podcast Settings" absolutely nothing happens.

If I click "Download All" absolutely nothing happens (nothing enters my download queue).

If I click "Show in iTunes Store" I go to a page saying that the Podcast could not be found.

There are similar questions in the 'iTunes for Windows' community but I'm using a Mac.