Pet Fee Question for Texas Landlords

[Account Closed]

Tenant here. Quick question for you landlords. I paid a non-refundable pet fee and a non-refundable deposit (half off what the typical deposit would have been). My cats did damage the carpet a bit, so two quick questions. 

Can a non-refundable pet fee be used for these damages, or is it supported that the fee is pretty much just for the "luxury" of having a pet on-site? 

In addition, I do not see my non-refundable deposit on the final statement of charges. When I opted to take the half off in exchange for making the deposit non-refundable, did I waive the option for that deposit to be used against any damages, or is that a mistake by my landlord which they should be responsible for? 

I appreciate your guidance,

Yale