If for any reason, you don’t want to promote your podcast, or you want to make sure your own website is the only place to find your podcasts, then you can easily hide your Buzzsprout public page from search engines.
Hide Your Buzzsprout Website From Search Engines
Just follow this process:
Go to your Website page.
Click the Hide from Search Engines tab.
Check Hide My Public Buzzsprout Website from Search Engines
Now your public page will request any web crawlers that find the page to not index it.