MoneyGram unwarranted charges Dallas Texas

I set up a MoneyGram account to pay a service provider in a foreign country.  The steps indicated on MoneyGram's website were all read through, and I agreed to the $14 per transaction to send money to my contact.  After 60 days, I checked my credit card bill.  MoneyGram requires you give them a bank account or a credit card to pay for the transaction.  Not wating to give my bank account information, I used a credit card (this is a Capital One credit card...not a debit card).  

When I audited my credit card account statement, I notice that Capital One had charged me $10 per transaction as a "cash advance".  I called them to ask why.  They put a supervisor on the phone, and he called MoneyGram while I was on the phone to ask the question.  MoneyGram's reply was that they consider this a "cash" transaction, and billed it that way to Capital One.

Now, I made the decision to use a credit card specifically to NOT use cash.  MoneyGram does not have thi sinformation in the automated sign up process so that an unsuspecting consumer can make an informed decision about how to pay for it.  But they refused to reverse the charges.

The Capital One supervisor also said that they can't do anything about it either, as they charge the $10 fee whenever there is a "debit" or "cash advance". 

This is unfair.  The fees I am paying, $60 over two months, make this an untenable situation for me.  My only recourse, as far as I know, is to discontinue using MoneyGram.  When I mentioned that to the rep, she indicated that the company does not care.