You mean the login box? Edit that same file and remove the codes below:
<?php if( !$this->my->id ){ ?>
<div class="es-login-box">
<div class="row-fluid">
<div class="span6 login-column">
<div class="login-wrap">
<form name="loginbox" id="loginbox" method="post" action="<?php echo JRoute::_( 'index.php' );?>">
<legend class="mt-20"><?php echo JText::_( 'COM_EASYSOCIAL_LOGIN_TO_ACCOUNT_TITLE' );?></legend>
<fieldset class="mt-20">
<input type="text" class="full-width" name="username" placeholder="<?php echo $this->config->get( 'registrations.emailasusername' ) ? JText::_( 'COM_EASYSOCIAL_LOGIN_EMAIL_PLACEHOLDER', true ) : JText::_( 'COM_EASYSOCIAL_LOGIN_USERNAME_PLACEHOLDER' , true );?>" />
<input type="password" class="full-width" name="password" placeholder="<?php echo JText::_( 'COM_EASYSOCIAL_LOGIN_PASSWORD_PLACEHOLDER' , true );?>" />
<label class="checkbox small mt-10">
<input type="checkbox"> <span class="small"><?php echo JText::_( 'COM_EASYSOCIAL_LOGIN_REMEMBER_YOU' );?></span>
</label>
<button type="submit" class="btn btn-es-success btn-block mt-20">
<?php echo JText::_( 'COM_EASYSOCIAL_LOGIN_TO_ACCOUNT_BUTTON' );?>
</button>
</fieldset>
<?php if( $this->config->get( 'oauth.facebook.registration.enabled' ) && $this->config->get( 'registrations.enabled' ) ){ ?>
<div class="center es-signin-social">
<p class="line">
<strong><?php echo JText::_( 'COM_EASYSOCIAL_LOGIN_SIGNIN_SOCIAL' );?></strong>
</p>
<?php echo $facebook->getLoginButton( FRoute::registration( array( 'layout' => 'oauthDialog' , 'client' => 'facebook', 'external' => true ) , false ) ); ?>
</div>
<?php } ?>
<hr />
<div class="center">
<a class="text-error" href="<?php echo FRoute::profile( array( 'layout' => 'forgetUsername' ) );?>"> <?php echo JText::_( 'COM_EASYSOCIAL_LOGIN_FORGOT_USERNAME' );?></a> /
<a class="text-error" href="<?php echo FRoute::profile( array( 'layout' => 'forgetPassword' ) );?>"> <?php echo JText::_( 'COM_EASYSOCIAL_LOGIN_FORGOT_PASSWORD' );?></a>
</div>
<input type="hidden" name="option" value="com_easysocial" />
<input type="hidden" name="controller" value="profile" />
<input type="hidden" name="task" value="login" />
<input type="hidden" name="return" value="<?php echo $return; ?>" />
<input type="hidden" name="returnFailed" value="<?php echo base64_encode( JRequest::getURI() ); ?>" />
<?php echo $this->html( 'form.token' );?>
</form>
</div>
</div>
<?php if( $this->config->get( 'registrations.enabled' ) ){ ?>
<div class="span6 register-column">
<div class="register-wrap">
<h3><?php echo JText::_( 'COM_EASYSOCIAL_LOGIN_NO_ACCOUNT' );?></h3>
<p class="center mb-20">
<?php echo JText::_( 'COM_EASYSOCIAL_LOGIN_REGISTER_NOW' );?>
</p>
<a class="btn btn-es-primary btn-large btn-block" href="<?php echo FRoute::registration();?>">
<?php echo JText::_( 'COM_EASYSOCIAL_LOGIN_REGISTER_NOW_BUTTON' );?>
</a>
</div>
</div>
<?php } ?>
</div>
</div>
<?php } ?>