Dealership refusing to give me a refund. Am I out of luck?

I’m a first time buyer in SC and I need some advice and clarification on a situation I’m currently stuck in.

I recently placed a $1,000 deposit at a dealership for a pre-owned vehicle I intended to purchase.

I received a purchase agreement & credit card authorization form. I never signed a purchase agreement or any kind of financing contract. The purchase agreement sent to me wasn’t what I agreed to before with finances. They claimed I will get the right one upon delivery.

The only thing I signed was a credit card authorization form. The authorization form I signed includes a clause stating I won’t dispute the payment “so long as the transaction corresponds to the terms indicated in this form.” But since no contract was signed and I never took delivery, I don’t think those conditions were fulfilled.

I backed out of the deal some days later after a few delays, inconsistent communication, and growing doubts about whether I was making the right financial choice.

When I spoke with the GSM about everything, he told me they would inform the bank the deal is off and that it’s their policy not to accept deposits on pre-owned vehicles. But a few days later, I followed up about the refund and was told there is no refund policy, and now they’re refusing to return the deposit. They’re also claiming I can still “take advantage of the deal” if I come get the car today even though I don’t want the car anymore.

Am I completely out of luck here?