Reply To: Taxonomy image on Search result

Based on the actual results page output, you could try something like:

<?php if ( !empty(get_asp_result_field('image') ): ?>
    <div class="img__wrap mb-3">
        <a href="<?php the_asp_result_field('link', true); ?>">
            <img class="img-fluid shadow-sm wp-post-image" src="<?php the_asp_result_field('image', true); ?>" />
        </a>
    </div>
<?php endif; ?>