Your problem is that

you only see the issue from your perspective, not customer's.

She paid and expected to get the item. She was charged extra $3.5 for it. If you were in that situation, you would do the same.

The lesson is how to avoid it in the future, but not how to fight the customer.

If you hold this attitude, the only person you are going to make it hard for is yourself.

Just my opinion and personal experiene. When I encountered this problem before, even the customer did not require refund, I would refund anyway for good will.