Credit card payment charge

so, I contacted Xfinity about using my credit card to auto pay my monthly bill instead of my checking account. I asked if there was a fee for using my credit card to which I was told no.

However, if I use my credit card versus my bank, I lose five dollars a month credit. 

if I pay using my bank with auto pay, I get a $10 a month credit.

do the math. There is a penalty if I use my credit card, which to me, is another way of saying that there is a charge for using my credit card.

I feel deceived, and I feel that this is an underhanded way for XFINITY to charge their people for using their credit cards to pay their monthly bills

Bad business.