You can try to add the follwing lines between ob_start() and ob_get_clean() calls of wooajaxcart.php file:
echo '<td class="product-remove">';
echo apply_filters( 'woocommerce_cart_item_remove_link', sprintf( '<a href="%s" class="remove" title="%s">×</a>', esc_url( WC()->cart->get_remove_url( $_POST['cart_item_key'] ) ), __( 'Remove this item', 'woocommerce' ) ), $_POST['cart_item_key'] );
echo '</td>';