How to remove the Template drop down, but keep Parent and Order

When you remove that box from admin (as you’ve written in the comment), you should be able to re-register that box with custom function (modified original) to render the box:

if ( post_type_supports($post_type, 'page-attributes') )
    add_meta_box('pageparentdiv', 'page' == $post_type ? __('Page Attributes') : __('Attributes'), 'my_page_attributes_meta_box', null, 'side', 'core');

function my_page_attributes_meta_box($post) {
    $post_type_object = get_post_type_object($post->post_type);
    if ( $post_type_object->hierarchical ) {
        $dropdown_args = array(
            'post_type'        => $post->post_type,
            'exclude_tree'     => $post->ID,
            'selected'         => $post->post_parent,
            'name'             => 'parent_id',
            'show_option_none' => __('(no parent)'),
            'sort_column'      => 'menu_order, post_title',
            'echo'             => 0,
        );

        $dropdown_args = apply_filters( 'page_attributes_dropdown_pages_args', $dropdown_args, $post );
        $pages = wp_dropdown_pages( $dropdown_args );
        if ( ! empty($pages) ) {
?>
<p><strong><?php _e('Parent') ?></strong></p>
<label class="screen-reader-text" for="parent_id"><?php _e('Parent') ?></label>
<?php echo $pages; ?>
<?php
        } // end empty pages check
    } // end hierarchical check.
    if ( 'page' == $post->post_type && 0 != count( get_page_templates() ) ) {
        $template = !empty($post->page_template) ? $post->page_template : false;
        ?>
<p><strong><?php _e('Template') ?></strong></p>
<label class="screen-reader-text" for="page_template"><?php _e('Page Template') ?></label><select name="page_template" id="page_template">
<option value="default"><?php _e('Default Template'); ?></option>
<?php page_template_dropdown($template); ?>
</select>
<?php
    } ?>
<p><strong><?php _e('Order') ?></strong></p>
<p><label class="screen-reader-text" for="menu_order"><?php _e('Order') ?></label><input name="menu_order" type="text" size="4" id="menu_order" value="<?php echo esc_attr($post->menu_order) ?>" /></p>
<p><?php if ( 'page' == $post->post_type ) _e( 'Need help? Use the Help tab in the upper right of your screen.' ); ?></p>
<?php
}

You can modify the function as much as you want to. The code of the function is taken from http://core.trac.wordpress.org/browser/tags/3.5.1/wp-admin/includes/meta-boxes.php#L618