You can remove this by going to "Appearance" > "Editor" then look for the Home Page Template (home-page.php). Click on it, find and then delete or hide this code:
<!-- Tweet-Like Buttons Starts Here -->
<div id="tweet-like"><div><a href="http://twitter.com/share" class="twitter-share-button" data-count="horizontal">Tweet</a><script type="text/javascript" src="http://platform.twitter.com/widgets.js"></script></div><div>
<div class="fb-like" data-href="<?php echo get_option($mobileSettings->prefix . 'social_network_url_facebook'); ?>" data-send="false" data-layout="button_count" data-width="450" data-show-faces="false"></div>
<?php /*?><iframe src="http://www.facebook.com/plugins/like.php?app_id=153282078076131&href=<?php bloginfo('url'); ?>&send=false&layout=button_count&width=450&show_faces=false&action=like&colorscheme=light&font=arial&height=21" scrolling="no" frameborder="0" style="border:none; overflow:hidden; width:100px; height:21px; position: relative; top: 1px;" allowTransparency="true"></iframe><?php */?></div></div>