you can add your own class under post loop item,

add_filter('post_grid_item_classes', 'post_grid_no_post_text_20200614', 10, 2);

function post_grid_no_post_text_20200614( $item_css_class, $args){
    
    $post_id = $args['post_id'] ;

    $item_css_class['custom-new'] = 'custom-class';

    return $item_css_class;

}

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Include post terms slug

add_filter('post_grid_item_classes', 'post_grid_no_post_text_20200614', 10, 2);

function post_grid_no_post_text_20200614( $item_css_class, $args){

    $post_id = $args['post_id'] ;

    $item_css_class['post_term_slug'] = post_grid_term_slug_list($post_id);


    return $item_css_class;

}