Will ATT reimburse me for credit card interest caused by their mistaken charge?

I am very frustrated and upset with AT&T's customer service. It is the worst service I've ever had with any company I've dealt with in over 50 years.

ATT mistakenly charged $99 to my credit card for an internet installation service that they charged me by accident. They admitted their mistake and are issuing me a refund, however, they say they can't put the money back on my credit card, and have to mail a check. They say it will take between 30-45 days. In the meantime, my credit card bill is due on Aug. 17th, and if I don't pay off the entire balance by the due date then the entire balance is charged an interest rate of 21.24%. I am very careful with my budget, and I don't have an extra $99 to pay off my credit card bill. And I shouldn't have had to budget for an ATT mistaken charge.

No one is any help. No one on the phone, and no ATT employees on here are any help - they just don't care.

Now will they reimburse me for the interest charges they caused me to have?