Display recent posts with thumbnail within Masonry

Add the meta_key parameter to fetch the latest posts which have featured image set. $args = array( 'numberposts' => '10', 'meta_key' => '_thumbnail_id' );

<?php
/* 
Template Name: Recent Profiles 
*/
get_header();
?>
<h1 class="page-title"><?php the_title(); ?></h1>

    <div id="content">
        <div id="masonry">
            <?php if ( have_posts() ) : while ( have_posts() ) : the_post(); ?>
                <div class="item normal" data-order="1"><!--BEGIN .item -->
                    <div <?php post_class(); ?> id="featured-<?php the_ID(); ?>"><!--BEGIN .hentry -->
                        <?php
                        $args = array( 'numberposts' => '10', 'meta_key' => '_thumbnail_id' );
                        $recent_posts = wp_get_recent_posts( $args );
                        foreach ( $recent_posts as $recent ) {
                            if ( has_post_thumbnail( $recent["ID"] ) ) {
                                echo '<a href="' . get_permalink( $recent["ID"] ) . '">';
                                echo get_the_post_thumbnail( $recent["ID"], 'archive_grid' );
                                echo '</a>';
                            }
                        }
                        ?>
                    </div>
                    <!--END .hentry-->
                </div><!--END .item -->
            <?php endwhile; endif; ?>
            <?php get_template_part( 'includes/index-loadmore' ); ?>
        </div>
        <!--END #masonry -->
        <div id="masonry-new"></div>
        <!--BEGIN .post-navigation -->
        <div class="post-navigation clearfix">
            <?php dt_pagination(); ?>
            <!--END .post-navigation -->
        </div>
    </div><!-- #content -->
<?php get_footer(); ?>

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