Don't understand your reasoning here. The deposit of $100 has been made, which is your reservation deposit and is not returnable, but is taken off your total rental contract amount when paid, when you pick up your car.
The bank are reimbursing for the fraudulent charges, so you are not our of pocket.
When you pay for the car contract (with whatever card you'll use) watch them do the transaction on the machine or use the POS/wifi option and then no phones, no talking, no phones, no problems.