I think the term you're looking for is negative billing. Reverse billing is used to describe charges for SMS/voice calls where the recipient pays for the charges.
Negative billing implies they added something without your permission, but you have the option to remove it to bring it down to the previous price point. This is not the case here. I don't think there's anything illegal for a business to raise prices and provide notice that they are doing so, and offering an option to leave.