First, I added a link and clicked on it, and then it showed up as a popular link on this topic:
Then I edited the reply and removed the link, and it removed it from the topic listing:
And so the solution to remove popular links is to literally remove the links from the discussion. 
If I wanted to remove certain links while retaining the info, I’d add backticks (`) on either side.
I read `https://en.wikipedia.org/wiki/Flour`!
Becomes:
I read
https://en.wikipedia.org/wiki/Flour!
And removes the link from the popular links list.
Hope that helps!