Hi! Thanks for writing! I will try to answer your question as best as I can to the extent I understand it! It is an interesting problem.
Since you write that your sister used the card number rather than the physical card, I'll assume that she bought something online. Let's say that she ordered a sweater online from Urban Outfitters for $50 and with shipping and tax the total was $60. She used your Capital One card, and the bill was posted to the card on 7-15-16. The bill came and you paid it on on 8-15-16 including the $60 from Urban Outfitters. Your sister then mailed the sweater back to Urban Outfitters on 9-20-16, and they credited your credit card for the cost of the sweater less the shipping, so you got a credit on your Cap One card for like $53 because the shipping doesn't get returned to you.
Did your sister give you $60 in cash after she used your card or give you something equivalent to $60? If so, then you would indeed owe her back the $60. In that case, you paid for the sweater and got the money back and your sister is out $60 with no sweater and you have her $60 in cash. However, if she didn't give you money for the sweater, then you wouldn't owe her any money back. In fact, technically she should give you the difference in the shipping that didn't get returned - in this example, $7.
I am trying to imagine what would make your sister think that you would owe her the $60 if she hadn't reimbursed for the use of your card, and I can't think of a reason. Maybe do your parents pay you and your sister's credit card bills and your sister is thinking that that $60 is due to her from your parents? That's the only way I can imagine that she would be due to get money back from you in this case!!
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