Since you did not yet receive the refund, you do not need to include payment as long as this is ONLY due to paying back some of the refund you already received and NOT because you would have had to pay in to start with. If this amount is higher than what you would have had refunded to you, then you will need to pay that amount with the amended return.
Generally, one should wait until the return is processed and then they already received the refund so they can just send some back. In your case, you are being told they are not processing your refund without the error being corrected. Once they receive your amended return, they will give you the lower refund amount.
If the amended return is giving you the option, you can choose mail paper check. This will allow you to submit without payment.
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