確認画面がないので、「未登録」処理が噛ませられないので、
更新時に、下記の様な感じで、強制設定、、、する、ですかね。。。

動作未確認です。(comu版での動作確認結果を2.4.4のコードへ反映まで)

data/class/pages/mypage/LC_Page_Mypage_DeliveryAddr.php

   function lfRegistData($array, $arrRegistColumn, &$objCustomer) {
       $objConn = new SC_DBConn();
       foreach ($arrRegistColumn as $data) {
           if (strlen($array[ $data["column"] ]) > 0) {
               $arrRegist[ $data["column"] ] = $array[ $data["column"] ];
           }
       }

       $arrRegist['customer_id'] = $objCustomer->getvalue('customer_id');

       //-- 編集登録実行
       $objConn->query("BEGIN");
       if ($array['other_deliv_id'] != ""){

           if(!isset($arrRegist["company_name"])){
               $arrRegist["company_name"] = null;
           }
           if(!isset($arrRegist["company_kana"])){
               $arrRegist["company_kana"] = null;
           }

           $objConn->autoExecute("dtb_other_deliv", $arrRegist,
                                 "other_deliv_id = "
                                 . SC_Utils_Ex::sfQuoteSmart($array["other_deliv_id"]));
       }else{
         $objConn->autoExecute("dtb_other_deliv", $arrRegist);
       }
       $objConn->query("COMMIT");
   }