How to exclude html links from WordPress search?

When running a search within WordPress it also seems to be picking up image links within the search leading to lots of unrelated articles being picked up. For example if the domain were example.com and you searched for “Example” it is finding any page that contains images or internal links in the HTML as the word example appears in the domain name being linked even though there is no other mention of the word “Example” within the content.

Is there any way to filter the search to ignore the HTML links? I can find many examples of plugins and code to remove pages or post types but nothing to ignore the raw HTML where it is purely functional.