You'll need to refund the payment to an Other payment method, then use the Other payment method to make a payment on the new reservation.

NOTE: This will not work on checked in or cancelled group sales.

To refund the payment
  1. Go to Sales Group Sales
  2. Go to the reservation the original payment was made on
  3. Go to Refunds, then click Add reservation refund
  4. On the refund change the Refund method to Other  
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  5. Add your Reason
  6. Click Complete Refund

To add the payment to the new order
  1. Go to Sales Group sales 
  2. Find your new group sale reservation
  3. Go to Add a payment
  4. Change the payment method to Other
  5. Specify which other method you used 
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  6. Click Save