A card holder's signature verifies that the transaction is legitimate. So essentially, in a sense, the card holder's signature must be demanded and and should be communicated in such a fashion so there is no question that any other signature will suffice.
Sorry, but the card holders signature is required to authorise payments.
It is polite to say 'sorry' at the start, this is not because you have done something wrong, it is to show empathy and understanding towards the customer and to give good service.
You can then go on to explain that the signature of the person that the card belongs to, the card holder, is required. Required, means that is is necessary.
Authorise means to give official approval for something, and in this case, the expressed approval of the card holder, by giving their signature, is needed.
you cannot make a purchase without the card holders signature
example
"Please provide the signature of the cardholder to allow
purchase to be made using this card."
or
"Purchase cannot be completed unless you have
the signature of the cardholder."
or
"We cannot process payment until we have a signature
from the cardholder.
"Please provide the signature of the cardholder to allow purchase to be made using this card."
このカードを使うには、カード名義人の署名を頂きます。
"Purchase cannot be completed unless you have the signature of the cardholder."
カード名義人の署名がないと、精算できません。
"We cannot process payment until we have a signature from the cardholder."
カード名義人の署名がないと、ご精算することができません。
The signature of the card holder is required when paying by credit card.
I'm sorry you can't use your mother's card because...
In this situation in England, we usually begin with an apology (but this isn't essential!). Then I would begin with the 'signature of the card holder'. A signature is a persons name written in a distinctive way. By adding 'of the card holder' you're emphasising that it has to be the owner of the card (in this case, the mother). 'Required' is a formal way of saying 'is needed'. And I would finish this sentence with 'when paying by credit card' to show that this is the only situation where a signature is required.
イングランドでは普通この状況では謝罪から入ります（必須ではありませんが）。
そうしたら、私ならまずは 'signature of the card holder'（カード名義人のサイン）で始めます。
'signature' は、本人であることを証明するために自分の名前を書くことをいいます。
'of the card holder' を加えて、それがカードの名義人のものでなければならないことを強調しています。
'required' は 'is needed'（必要とされる）のフォーマルな言い方です。
最後に 'when paying by credit card'（クレジットカードで払うとき）と言って、署名が求められるのはその状況だけであることを伝えています。
In order to authorize payment with the credit card, the card holder must be present to sign.
The owner of the credit card must be present in order to sign and validate the purchase.
I signature from the card owner must be acquired in order to complete the purchase.
To authorize means to give approval for the purchase being made. This will protect the credit card holder from having to pay for purchases that he/she did not give permission to make.
"The owner" refers to the person who is named on the credit card and has signed the back of it. This is the only person who can use the card for purchases, and therefore, he/she would need to sign for the purchase in person. It is customary for the credit card holder to be able to provide identification in order to show that he/she is the owner of the card.
When acquiring a signature, the person making the sale must have the card owner place his/her signature on a form of documentation, typically a receipt, in order to complete the sale. If this step is not taken, then the charge is not valid.
"To authorize" は「購入に許可を与える」という意味です。これにより、カードの保有者が自らの知らない支払いをすることがなくなります。
"The owner"（所有者）とは、クレジットカードに名前が書かれた人のことです。カードの裏側にはこの人が署名をしますね。カードを使うことのできるは所有者だけです、ですから何かを買う際にはこの人が自ら署名をしなければなりません。クレジットカードの保有者は自らがその所有者であると証明できるよう普通身分証明書を用意しています。
お店はカードの所有者に文書（普通はレシート）に署名をさせなければ商品を売ることができません。この手続きが行われていないと請求は無効になります。
Unfortunately, the owner of the card needs to sign in order for the transaction to be processed.
It is very easy for credit cards to be misused by the wrong people. Therefore as a means of security for the business, they require a signature from the person whose name the card is under in order for a purchase or payment to be made.
アメリカ合衆国 
イギリス 
南アフリカ 
