Welcome to the Community, @lena21.

You can refund your customer's checking account by signing in to QuickBooks Payments and then reverse the transaction from the Processing Tools drop-down. There you can search for the transaction and select the sale you want to refund.

Let me show you how:

1. Sign in to your QuickBooks Payments account.
2. From the Processing Tools drop-down, select Reverse a Transaction.
3. Fill out the necessary fields and select Search.
4. Select the transaction(s) you want to refund, then Submit.

However, if you aren't subscribed to QuickBooks Payments, you can use refund receipts. Make sure you haven't created a credit memo because this would cause a double refund.

Here's how:

1. Select + New.
2. Select Refund receipt or Give refund.
3. Select the Customer ▼ dropdown, then select the customer you want to refund.
4. Select the Refund From ▼ drop-down, then select the bank you deposited the payment for the invoice too.
5. Add all products or services the customer returned in the Product or service column.
6. Make sure to fill the quantity, rate, amount, tax, and other fields accordingly, then select Save and close.

I'll add this video article as your guide in recording refunds based on various scenarios: Record a customer refund in QuickBooks Online. It includes how to refund a customer's overpayment.

If you wanted to learn more about alternative ways in processing refunds in QuickBooks Payments, here's your reference: Void or refund transactions in QuickBooks Payments.

Please let me know if you have more questions. I'll keep my notifications open. Have a good one!

Thanks for the answer , but it did not clarify my question.
  Similar was already in your Q / A .

 But my question is specifically about  a reverse the transaction  (made  not  today, but earlier  )  to  customer's checking account   (NOT  CREDIT CARD)
The first part of your answer applies only to Credit Card Transactions
 

          Credit card transactions

                       Charge a card
                       Reverse a transaction
                       Authorize funds
                      Capture authorized funds

And the second part of your answer means only a formal record of the return without its banking action (maybe we just don’t have this function?)

Today we have to make a refund of money , withdrawn from the customer’s checking  account,   with a check sent by mail.

Perhaps we don’t  fully understand  something.

Nash Dom

Thanks for getting back to us, @lena21.

In QuickBooks Online (QBO), there are only two ways on how to process a refund to a customer which was already shared by my colleague above. Since your customer is not using a credit card, I suggest looking for a third-party application as a workaround.

This can be done by going to the  Apps tab in the left panel, and enter a keyword in the search field. You can also click this link provided above for any apps you can find that’s integrated with QuickBooks: https://apps.intuit.com/app/apps/home.

Just in case, I'll add this article for future reference: Record a customer refund in QuickBooks Online.

Reach out to me in the comment section below if you have any other questions or concerns, and I'll get back to you as soon as possible. I'm always here to help. Have a great day!