Highlighted hyperlinks makes linked text unreadable

I am looking for a solution for the following problem;

I had several posts in draft when I made the change over to this theme. I published one of those posts and now they have a blue highlighted box around each of the texts with hyperlinks. I previewed the other 4 drafts and they are showing the same thing. The effect looks tacky and makes the text unreadable.

The only common cause I can see is that these were cut and pasted from an original post into a new post for clarity. The original post is fine and doesn’t have a highlighted box around any of the links.