JSFiddle - React, Tailwind, and code Playground

HTML

<script src="https://code.jquery.com/jquery-2.2.4.min.js"></script>
<div class="search search-results">
    <article id="post-1">News ** <a href:"#">This is the news text we need to process</a> **    hg Lorem ipsum dolor sit amet, consectetur adipiscing elit. Fusce at elit quis dui pretium ullamcorper id sit amet sapien. Nunc pharetra nisl sed libero pellentesque, et venenatis ex varius. Sed mattis vitae orci a imperdiet. Curabitur sollicitudin arcu ac metus condimentum, et hendrerit lorem sagittis. Nunc aliquam in dui eu dapibus. Phasellus sit amet sapien quis massa pulvinar elementum. Praesent elementum sem cursus, vehicula velit vel, hendrerit leo.</article>
    <article id="post-2">News ** This is the news text we need to process **    Lorem ipsum dolor sit amet, consectetur adipiscing elit. Fusce at elit quis dui pretium ullamcorper id sit amet sapien. Nunc pharetra nisl sed libero pellentesque, et venenatis ex varius. Sed mattis vitae orci a imperdiet. Curabitur sollicitudin arcu ac metus condimentum, et hendrerit lorem sagittis. Nunc aliquam in dui eu dapibus. Phasellus sit amet sapien quis massa pulvinar elementum. Praesent elementum sem cursus, vehicula velit vel, hendrerit leo.</article>
</div>

CSS

.search-results{
  width:100%;
  border:solid 1px black;
}
article{
  width:100%;
  margin-bottom:5px;
  box-sizing:border-box;
  padding:5px;
}

JavaScript

jQuery(function() {
    jQuery('.search-results').find('article[id*="post-"]').each(function() {
	    jQuery('#' + jQuery(this).attr('id')).html(jQuery(this).html().replace(/News \*\* .+? \*\*/g, ''));
    });
});