Hello Andy,

I am really sorry for the delay of this reply as it is a weekend for us here.
If I'm not wrong, are you set the Easyblog member dashboard menu item in your frontend?
If yes, you can set the menu item access only available for registered user, so the menu item only appear who user is logged in.

If you're not referring this, you can remove the code from this file -> JoomlaFolder\components\com_easyblog\themes\default\guest.login.php
Remove this LINE 54 - 56

			<li class="float-r">

				<a href="<?php echo EasyBlogHelper::getRegistrationLink();?>"><?php echo JText::_('COM_EASYBLOG_CREATE_AN_ACCOUNT'); ?></a>

			</li>

Hope this help.