How to filter posts by Letter in Wordpress only in $ _GET mode

Hello, I would like your help to be able to add to the code below a correction that performs alphabet filtering with letters from # to Z, only when the $_GET['letra'] parameter is executed, if it is not executed, show all the existing items, while also maintaining the current paging system operation, in both modes.

Code

 <?php
/*
Template Name: DT - Animes Legendados
*/
get_header();
doo_glossary('tvshows');
global $user_ID;
$dt = isset( $_GET['get'] ) ? $_GET['get'] : null;
$admin = isset( $_GET['admin'] ) ? $_GET['admin'] : null;
echo '<div class="module"><div class="content">';
get_template_part('inc/parts/modules/featured-post-tvshows');
echo '<div id="archive-content" class="animation-2 items calendario">';



// Ordenar em ordem alfabetica
global $wp_query;
$pages = $wp_query->max_num_pages;

$first_char = $_GET['letra'];

$postids=$wpdb->get_col($wpdb->prepare("
SELECT      ID
FROM        $wpdb->posts
WHERE       SUBSTR($wpdb->posts.post_title,1,1) = %s
ORDER BY    $wpdb->posts.post_title",$first_char)); 

query_posts(array(
    'post__in'      => $postids,
    'posts_per_page' => $pages,
    'caller_get_posts'=> 1,
    'paged' => $paged,
    'post_status'   => 'publish',
    'post_type'     => array('tvshows'),
    'meta_key'      => 'tipo_de_media',
    'meta_value'    => 'Lista',
    'order'         => 'ASC',
    'orderby'       => 'title'
));
if (have_posts()) {
echo '<header><h1>'. __d('Listagem'). '</h1><span>Total ('.$wp_query->found_posts . ')</span></header>';
    while (have_posts()) {
        the_post();
        get_template_part('inc/parts/item');
    }
}else { echo '<header><h1>'. __d('Doramas'). '</h1><span>Total ('.$wp_query->found_posts . ')</span></header>';
echo '<div class="wp-content">
<blockquote><p>No momento essa seção esta sem nenhum conteúdo, em breve ela sera ativada.</p></blockquote>
</div>'; }
echo '</div>';
if ( function_exists("pagination") ) {
    pagination();
}
echo '</div>';
get_template_part('inc/parts/sidebar');
echo '</div>';
get_footer();

Paging function

if( ! function_exists( 'pagination' ) ) {
    function pagination($pages = '', $range = 2) {
        $showitems = ($range * 2)+1;
        global $paged;
        if(empty($paged)) $paged = 1;
        if($pages == '') {
            global $wp_query;
            $pages = $wp_query->max_num_pages;
            if(!$pages) {
                $pages = 1;
            }
        }
        if(1 != $pages)  {
            echo "<div class=\"pagination\"><span>". __d('Page') ." ".$paged." " . __d('of') . " ".$pages."</span>";
            if($paged > 2 && $paged > $range+1 && $showitems < $pages) echo "";
            if($paged > 1 && $showitems < $pages) echo "<a class='arrow_pag' href='".get_pagenum_link()."'><i id='prevpagination' class='icon-caret-left'></i><i id='prevpagination' class='icon-caret-left'></i></a>";        
            if($paged > 1 && $showitems < $pages) echo "<a class='arrow_pag' href='".get_pagenum_link($paged - 1)."'><i id='prevpagination' class='icon-caret-left'></i></a>";

            for ($i=1; $i <= $pages; $i++) {
                if (1 != $pages &&( !($i >= $paged+$range+1 || $i <= $paged-$range-1) || $pages <= $showitems )) {
                    echo ($paged == $i)? "<span class=\"current\">".$i."</span>":"<a href='".get_pagenum_link($i)."' class=\"inactive\">".$i."</a>";
                }
            }

            if ($paged < $pages && $showitems < $pages) echo "<a class='arrow_pag' href=\"".get_pagenum_link($paged + 1)."\"><i id='nextpagination' class='icon-caret-right'></i></a>";
            if ($paged < $pages && $showitems < $pages) echo "<a class='arrow_pag' href=\"".get_pagenum_link($pages)."\"><i id='nextpagination' class='icon-caret-right'></i><i id='nextpagination' class='icon-caret-right'></i></a>";                 
        if ($paged < $pages-1 &&  $paged+$range-1 < $pages && $showitems < $pages) echo "";
            echo "</div>\n";
            echo "<div class='resppages'>";
            previous_posts_link('<span class="icon-chevron-left"></span>');
            next_posts_link('<span class="icon-chevron-right"></span>');
            echo "</div>";
        }
    }
}