Simply put, there isn't enough information here to definitively say whether there's a GDPR violation here – taking the customer's personal info could have all sorts of GDPR-compliant purposes here, such as:
Taking the customer's info for purposes of raising the case for the refund request, and subsequently logging that it was declined due to lack of receipt.
Taking the customer's info for purposes of seeing if the original sale can be found in the system (therefore obviating the need for the receipt). If the info can't be found, the refund is then declined due to lack of receipt.
I could go on. The point is that GDPR is not something that means giving your personal info to an organisation means they have to give you the outcome you require.
Of course the data subject would be entitled to ask why they needed their personal info, what they used that for, and what they have retained (that's the transparency part) and they may even be able to ask that the data be removed if there's no overriding requirement for retaining it.