JSFiddle - React, Tailwind, and code Playground
HTML
<li class="up-sells">
<h2>How can I remove this text?</h2>
<ul class="bar">
<li><a href="#">Link</a></li>
</ul>
</li>
JavaScript
$('.up-sells').contents().filter(function(){
return (this.nodeType == 3);
}).replace('this text');