Hi Dee Gladney,
You can use this method and overwrite the markup
http://docs.joomla.org/How_to_override_the_output_from_the_Joomla!_core
You will have this file in your template folder.
\html\com_content\article\default.php
And it is easy to change $canEdit value to false.
$canEdit = $this->item->params->get('access-edit');
=>
$canEdit = false;
Hope it helps,
Regards