As you didn't ask them to pay the fine and they paid it without asking you first, 'demanding' reimbursement afterwards seems unrealistic, even if they did it as a favour.
How did they get the parking ticket? Was it sent to you and they picked it up, or is the car registered in their name so that it went to them? As dzug says, if it's a rental company they're entitled to pay it and charge you. You will have signed a document when you took the car on authorising them to do just that. In addition, they will have the authority to take it from your card.