JSFiddle - React, Tailwind, and code Playground
HTML
<link rel="stylesheet" href="http://ajax.googleapis.com/ajax/libs/jqueryui/1.8.4/themes/ui-lightness/jquery-ui.css">
<ul>
<li class="rss-item">
<a class="rss-item" href="http://myblog.com/post-title">Post Title</a>
<br>
http://myblog.com/post-title/Post Title <!-- this line I want to remove -->
<div class="thumbnail">
<a href="#">
<img src="thumbnail.jpg">
</a>
</div>
<div class="excerpt">Excerpt text</div>
<a href="http://myblog.com/post-title">Continue reading...</a>
</li>
</ul>
JavaScript
var tn = $('a.rss-item[href="http://myblog.com/post-title"] + br')[0].nextSibling;
tn.parentNode.removeChild( tn );