I figured it out. For those wondering how to do this…
— Go to the plugin, and edit..
— Go to image-caption-hover/plugin.class.php
— Change this; <a href="<?php echo $btn_link; ?>" target="_blank"><?php echo $btn_text; ?></a>
— To This; <a href="<?php echo $btn_link; ?>" target="_self"><?php echo $btn_text; ?></a>