My Boss Is Making Me Pay For Uniform Cleaning After I Quit, Is This Legal?

Location: Dallas, Texas and honestly not sure if what my former employer is doing is allowed. I worked at a high end restaurant for about 8 months until I quit two weeks ago (gave proper notice).
So here's what happened. When I started they gave me two chef coats and said the restaurant covers dry cleaning costs. Every week I'd drop them off at the place they use and they'd handle the bill directly. Never had any issues with this arrangement the whole time I worked there.
Now that I've quit, the manager called me yesterday saying I owe them $340 for "outstanding uniform cleaning charges" and that they're gonna send me a bill. When I asked what charges, she said it was for the last month of cleaning plus some kind of "final cleaning fee" for the uniforms I returned.
This seems really sketchy to me because I returned both coats when I quit and they were clean. I had actually saved up money to buy my own chef gear for my new job so I didn't even need to keep their uniforms. The whole reason I had some savings set aside was because I knew I'd need new work clothes.
I looked through my paperwork from when I was hired and there's nothing about paying cleaning costs if you quit. The employee handbook just says "uniforms provided, cleaning arranged by management."
My questions:
-Can they suddenly make me pay for cleaning that they covered while I was employed? - What's this "final cleaning fee" about, is that even a real thing?
- Should I just pay it or fight it?

The amount isn't gonna break me but it's still a lot of money and I feel like they're just trying to get extra cash out of me because I quit.