You don't get to write off something you didn't incur. If you buy something that is $100 for $80, all you incurred is $80. The "owner" giving it as cash or a coupon or a gift card, didn't "give" them $100. It is $80 value for $80 spent.

The owner seems to want to make the difference as payable to him/her, but there was no difference.

Let's try it like this: The Owner pays for something for business and turns in the receipt and the something. They get reimbursed under an accountable plan. That is repaid at the cost of what got spent; not some higher value it could have sold for, and not the difference.