The short answer? You cannot click on those links and they are not there to begin with. The reason you can read that text is lazy content management on the podcast production side; nothing more and nothing less.
The longer answer? Read on… The text you are referencing comes from the summary
or description
XML data field in the publisher’s iTunes RSS XML feed. To better understand the overall way one creates a podcast for iTunes, check this comprehensive document as well as the RSS 2.0 spec here. Here is the recommendation on the usage of the <itunes:summary>
and <description>
tags:
Take advantage of the <itunes:summary>
tag. The <itunes:summary>
tag
(or the <description>
tag if <itunes:summary>
is not present) allows
you to inform users about your podcast. Describe your subject matter,
media format, episode schedule, and other relevant information. In
addition, make a list of the most relevant search terms for your
podcast and build them into your description. Note that the iTunes
Store removes podcasts that include irrelevant words in the
<itunes:summary>
or <description>
tags.
Now, nothing in these specs explicitly references disallowing links within summaries/descriptions but I do know from being a web developer that RSS feeds can be messy to deal with to say the least. Meaning, in general, RSS feeds—and not just podcasts—are not meant to be full replacements for content; they simply act as a way to convey a quick “Hey, check out this stuff!” information about something. In this case, a podcast episode with the only link being the link to the actual podcast itself.
So my gut tells me the reason you are seeing “click here” text is a simple result of lazy content management practices on the podcast publisher’s side. Meaning looking at the specific TLDR episode (#44, “Prostitute Laundry”) on their actual website shows the following; screenshot attached for reference:

And all of those links are indeed active on their website, but not in the podcast info. Meaning that the way WNYC seems to be generating podcast RSS XML data is by taking the “description” that is used for their blog post, stripping out links and extraneous HTML and repurposing it—dual purposing it?—for the podcast description/summary RSS XML datapoints. A more content-aware way of doing something like this would be to have a separate “Podcast Description” field in their content management system, but that would mean someone would have to essentially write two descriptions for each podcast which might be too time consuming.
Which is all to say, the text might be saying “click here” but not only is there no way to remedy that on the user end, the core reason comes down to the podcast content producer’s not making much of an effort to tailor their summary/descriptive content for different media/audiences. So when you say this:
Maybe they are just copy/pasting text from their website and not
properly coding the episode description.
You are on the right track, but it’s more automated than “cut and paste” it seems. I would say the RSS XML generation code they are using simply grabs the description text from their database, strips the links and then sets that as the “description”/“summary” for the iTunes XML feed.