ギャラリーのaタグにclassを追加したい

お世話になります。
ギャラリーのカスタマイズをしておりまして、
自動生成されるaタグにclassを入れたいと思い、以下のコードを
functions.phpに書きましたがどうしてもclassが入ってくれません。
なんとか調べてみましたがドンづまってしまいました。
どうすればclassが入れられるのかご教授ください！
何卒よろしくお願いいたします。

remove_shortcode('gallery', 'gallery_shortcode');    //デフォルトのショートコードの削除
add_shortcode('gallery', 'my_gallery_shortcode');

function my_gallery_shortcode( $attr ) {
	$post = get_post();

	static $instance = 0;
	$instance++;

	if ( ! empty( $attr['ids'] ) ) {
		// 'ids' is explicitly ordered, unless you specify otherwise.
		if ( empty( $attr['orderby'] ) ) {
			$attr['orderby'] = 'post__in';
		}
		$attr['include'] = $attr['ids'];
	}

	/**
	 * Filter the default gallery shortcode output.
	 *
	 * If the filtered output isn't empty, it will be used instead of generating
	 * the default gallery template.
	 *
	 * @since 2.5.0
	 * @since 4.2.0 The <code>$instance</code> parameter was added.
	 *
	 * @see gallery_shortcode()
	 *
	 * @param string $output   The gallery output. Default empty.
	 * @param array  $attr     Attributes of the gallery shortcode.
	 * @param int    $instance Unique numeric ID of this gallery shortcode instance.
	 */
	$output = apply_filters( 'post_gallery', '', $attr, $instance );
	if ( $output != '' ) {
		return $output;
	}

	$html5 = current_theme_supports( 'html5', 'gallery' );
	$atts = shortcode_atts( array(
		'order'      => 'ASC',
		'orderby'    => 'menu_order ID',
		'id'         => $post ? $post->ID : 0,
		'itemtag'    => $html5 ? 'figure'     : 'ul',
		'icontag'    => $html5 ? 'div'        : 'li',
		'captiontag' => $html5 ? 'figcaption' : 'p',
		'columns'    => 3,
		'size'       => 'det_visual',
		'include'    => '',
		'exclude'    => '',
		'link'       => 'file'
	), $attr, 'gallery' );

	$id = intval( $atts['id'] );

	if ( ! empty( $atts['include'] ) ) {
		$_attachments = get_posts( array( 'include' => $atts['include'], 'post_status' => 'inherit', 'post_type' => 'attachment', 'post_mime_type' => 'image', 'order' => $atts['order'], 'orderby' => $atts['orderby'] ) );

		$attachments = array();
		foreach ( $_attachments as $key => $val ) {
			$attachments[$val->ID] = $_attachments[$key];
		}
	} elseif ( ! empty( $atts['exclude'] ) ) {
		$attachments = get_children( array( 'post_parent' => $id, 'exclude' => $atts['exclude'], 'post_status' => 'inherit', 'post_type' => 'attachment', 'post_mime_type' => 'image', 'order' => $atts['order'], 'orderby' => $atts['orderby'] ) );
	} else {
		$attachments = get_children( array( 'post_parent' => $id, 'post_status' => 'inherit', 'post_type' => 'attachment', 'post_mime_type' => 'image', 'order' => $atts['order'], 'orderby' => $atts['orderby'] ) );
	}

	if ( empty( $attachments ) ) {
		return '';
	}

	if ( is_feed() ) {
		$output = "\n";
		foreach ( $attachments as $att_id => $attachment ) {
			$output .= wp_get_attachment_link( $att_id, $atts['size'], true ) . "\n";
		}
		return $output;
	}

	$itemtag = tag_escape( $atts['itemtag'] );
	$captiontag = tag_escape( $atts['captiontag'] );
	$icontag = tag_escape( $atts['icontag'] );
	$valid_tags = wp_kses_allowed_html( 'post' );
	if ( ! isset( $valid_tags[ $itemtag ] ) ) {
		$itemtag = 'ul';
	}
	if ( ! isset( $valid_tags[ $captiontag ] ) ) {
		$captiontag = 'p';
	}
	if ( ! isset( $valid_tags[ $icontag ] ) ) {
		$icontag = 'li';
	}

	$columns = intval( $atts['columns'] );
	$itemwidth = $columns > 0 ? floor(100/$columns) : 100;
	$float = is_rtl() ? 'right' : 'left';

	$selector = "thumbs";

	$size_class = sanitize_html_class( $atts['size'] );
	$gallery_div = "<div id='$selector' class='navigation gallery galleryid-{$id} gallery-columns-{$columns} gallery-size-{$size_class}'>";

	/**
	 * Filter the default gallery shortcode CSS styles.
	 *
	 * @since 2.5.0
	 *
	 * @param string $gallery_style Default CSS styles and opening HTML div container
	 *                              for the gallery shortcode output.
	 */
	$output = apply_filters( 'gallery_style', "
	<div id='gallery' class='content'>
		<div class='slideshow-container'>
			<div id='loading' class='loader'></div>
			<div id='slideshow' class='slideshow'></div>
		</div>
	</div>
	<div id='thumbs' class='navigation'>
		<ul class='thumbs noscript'>
  ");

	$i = 0;
	foreach ( $attachments as $id => $attachment ) {

		$attr = ( trim( $attachment->post_excerpt ) ) ? array( 'aria-describedby' => "$selector-$id" ) : '';
		if ( ! empty( $atts['link'] ) && 'file' === $atts['link'] ) {
			$image_output = wp_get_attachment_link( $id, $atts['size'], false, false, false, $attr );
		} elseif ( ! empty( $atts['link'] ) && 'none' === $atts['link'] ) {
			$image_output = wp_get_attachment_image( $id, $atts['size'], false, $attr );
		} else {
			$image_output = wp_get_attachment_link( $id, $atts['size'], true, false, false, $attr );
		}
		$image_meta  = wp_get_attachment_metadata( $id );

		$orientation = '';
		if ( isset( $image_meta['height'], $image_meta['width'] ) ) {
			$orientation = ( $image_meta['height'] > $image_meta['width'] ) ? 'portrait' : 'landscape';
		}

    $link =  wp_get_attachment_link($id, $size, false, false);
    $link=str_replace('<a ','<a class="thumb" ', $link);

		$output .= "
			<{$icontag}>
				$image_output
			</{$icontag}>";
	}

	$output .= "
		</ul>\n</div>\n<div class='clear'></div>\n";

	return $output;
}