Texas Landlord Wants To Charge Reletting Fee Across Remainder Of Months In Lease As A Penalty, Is This Legal.

I broke my lease with 9 months left, the reletting fee is $800. I gave 30 days notice of early termination and paid the fee. However, they are saying that the reletting fee is multiplied by all the months remaining in the contract. So they want $7200 for breaking the lease early. This far exceeds their actual damages to boot. I had given them the keys for the unit on the fifteenth of the month, even after paying the full month's rent. There's no way it would cost them near that much to relet the unit.

My preliminary review of the law reveals that a landlord cannot charge damages in excess of their costs, yet they are attempting to do so brazenly. I also argue that it is no way explicitly stated, or reasonably expected in my contract, that the reletting fee would be charged for all the remaining months on the lease.

Do i have a case here.