Question on service costs for a secondhand car from a dealer

Hoping someone can offer some advice. Purchased a car from a dealership just under 2 months ago, car was MOT'd before sale and had new brake discs installed. I took out extended warranty on car. First 1000 miles and scraping noise as well as grinding when in reverse, then handbrake button comes off which stops handbrake locking into place.

Contact dealer who sends me to his garage that did MOT and brakes. I give them the warranty stuff to deal with and email from warranty provider comes back. Loose brake dust covers, then handbrake needs replacing. £280 total with warranty provider covering £250 of it. I know it's only £30 ish but should I be expected to pay anything given this. Under UK law, I thought the dealer should have been responsible, and would the brake covers being loose be something that resulted from the discs being changed. I was also surprised that the whole handbrake needed replacing given it was just the button, a common issue with that model that apparently can be sorted with a button and grub screw.

I am relatively new to cars. Car in question is a 13yr old Seat Leon hatch. Service history was about as flawless as it gets with everything done on time. 100% Mot pass with all advisories getting sorted as they were picked up. Always had oil and filter changes ect.