Change the ElasticPress search query to match only content with a thumbnail set.

elasticpress-search-thumbnail-exists.php

<?php
/**
 * Since ElasticPress 4.0, thumbnails are indexed in a separate field.
 */
add_filter(
	'ep_post_formatted_args',
	function ( $formatted_args ) {
		if ( empty( $_GET['has_image'] ) ) {
			return $formatted_args;
		}
		$formatted_args['post_filter']['bool']['must'][] = array(
			'exists' => array(
				'field' => 'thumbnail',
			),
		);
		return $formatted_args;
	}
);