Hello William

You can hide the registration button by comment or remove these code in ...\components\com_easydiscuss\themes\simplistic\form.reply.login.php

		<div class="span7">

			<div class="media">

				<div class="media-object pull-left">

					<img src="<?php echo JURI::root();?>components/com_easydiscuss/themes/simplistic/images/icon-locked.png" alt="<?php echo JText::_( 'COM_EASYDISCUSS_LOGIN_IMAGE' , true );?>" />

				</div>

				<div class="media-body small">

					<h4><?php echo JText::_( 'COM_EASYDISCUSS_PLEASE_LOGIN_TO_REPLY_TITLE' );?></h4>

					<p><?php echo JText::_( 'COM_EASYDISCUSS_PLEASE_LOGIN_TO_REPLY_INFO' );?></p>

					<a href="<?php echo DiscussHelper::getRegistrationLink();?>" class="btn btn-success mt-10"><?php echo JText::_( 'COM_EASYDISCUSS_REGISTER_HERE' );?></a>

				</div>

			</div>



		</div>

Hope this help