How to override this theme function in child theme

You can’t override the function(s). They aren’t meant to be overwritten. See: “Override parent theme function that is not hooked or in the functions.php file” and “Is it possible to disable a function of a parent theme?”. That is the direct answer to your question.

You can, however, almost certainly achieve the result you want by using the filter provided by the theme– udesign_get_top_main_menu— or any number of filters provided by wp_nav_menu() or by the Walker_Nav_menu class— perhaps wp_nav_menu_objects or wp_nav_menu_items.

Per the question, you are wanting to remove:

$menu_html .= is_front_page() ? "<li class="current_page_item">" : "<li>";
$menu_html .= '<a href="'.home_url().'"><span>'.esc_html__('Home', 'udesign').'</span></a></li>';

Ok. You probably need to use the filter provided in the code posted:

function udesign_strip($menu) {
  var_dump($menu);
  $menu_html = is_front_page() ? "<li class="current_page_item">" : "<li>";
  $menu_html .= '<a href="'.home_url().'"><span>'.esc_html__('Home', 'udesign').'</span></a></li>';
  $menu = str_replace($menu_html,'',$menu);
  return $menu;
}
add_filter('udesign_get_top_main_menu','udesign_strip');

I don’t like str_replaceing markup but that is probably the best way in this case.

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