Can I enter the refund as a deduction?
Yes. If this is a SCH C business, then one of the screens (I think it's in the income section) will ask you for amounts you gave back to clients/customers. You'll enter it there.
If this is a SC H E business, you'll enter it as a miscellaneous expense, and make sure you clearly label it as a client/customer refund.
Since you have the statements to back up your claim in case of an audit, I don't see any issues here.
