Issuance of credit-note u/s 34 (1) is optional. And in place of credit-notes u/s 34 (1), you can issue "accounting" credit-notes to settle books of accounts.
It is my understanding that your customer is asking you to pay the GST amount with interest, presumably because they have not books your credit-notes in their books earlier and thereby, they have NOT reversed ITC against your credit-notes.
I see at-least two solutions to this:
Whether GST portal is allowing you to cancel credit-notes u/s 34 (1) so issued OR make tax amount therein as zero? If yes, you can do that & pay back tax-amount (i.e. against re-credit taken earlier) - preferably in cash with interest to avoid another reason of controversies / disputes with Dept - while filing return.
Another option is that you can request your customer to reverse the proportionate ITC (against your credit-notes u/s 34 (1)) and make accounting debit-note for differential amount (in addition to earlier debit-note). This will match the books of accounts. If you want (for maintaining business reasons or if you have not presented those credit-notes to your customer in time etc.), you can also agree to bear cost of 'interest' to be paid by your customer towards delay in reversing ITC.
If none of above option works or acceptable to your customer, please let me know the reasons / difficulties to follow any of these options. And I will see what can be really done.
These are ex facie views of mine and the same should not be construed as professional advice / suggestion.