Hello John,
The compose button is view-able by users who has access to compose blog post. If you need to remove this, you could modify the theme file /components/com_easyblog/themes/wireframe/toolbar/default.php and remove the codes below,
[gist]
<?php if ($this->acl->get('add_entry')) { ?>
<div class="o-nav__item">
<a class="o-nav__link eb-navbar__icon-link" href="<?php echo EB::_('index.php?option=com_easyblog&view=composer&tmpl=component'); ?>"
data-eb-provide="tooltip" data-placement="top" data-original-title="<?php echo JText::_('COM_EASYBLOG_TOOLBAR_NEW_POST_TIPS');?>"
>
<i class="fa fa-pencil"></i>
<span class="eb-navbar__link-text"><?php echo JText::_('COM_EASYBLOG_TOOLBAR_NEW_POST');?></span>
</a>
</div>
<?php } ?>
[/gist]