Retailers get charged at least 2.5% for accepting credit card payments.
By paying off the loan early, the loan company is losing money on interest they would have otherwise received.
And then to pay 2.5% to the credit card company to accept her payment would be just too much. It is not not their interests.
Your credit card company wants your business - so you can ask them to pay off the loan (no cost to the loan company) - but the credit card company may charge you up to 3% to do so, usually capped at around �75 - �100.