How to remove an item from a custom Walker_Nav_Menu

I am still not sure how you call the menu or what $args you supply for the menu. But could suggest you some way to figure it out.

first test: return an empty array, if menu becomes empty, the filter is running,

if not, then your filter is not running and need to find another way

function wpse31748_exclude_menu_items( $items, $menu, $args ) {
    return [];
}
add_filter( 'wp_get_nav_menu_items', 'wpse31748_exclude_menu_items', null, 3 ); 

---

assume the filter is running, then probably your test logic have problem

function wpse31748_exclude_menu_items( $items, $menu, $args ) {

    // Iterate over the items to search and destroy
    $found_key = null;
    foreach ( $items as $key => $item ) {
        if ( $item->object_id == 6927 ) {
          // unset( $items[$key] ); // unset a iterating array is not a good idea and may lead to bug sometimes
          $found_key = $key; // handle it later.
        }
    }

    var_dump($found_key); // make sure you find something

    var_dump($items); // to compare before and after removal if it found something
    unset( $items[$found_key] );
    var_dump($items);

    return $items;
}

add_filter( 'wp_get_nav_menu_items', 'wpse31748_exclude_menu_items', null, 3 );