Not paying for Battery invoice

I received the most horrible service at Ford Claremont. I bought a second hand car from ford in March 2020 just before lockdown. Beginning of November 2020 the car had a mechanical breakdown and couldn’t start, it was towed into Ford Claremont on a Saturday. Thursday following week nobody had checked on the car until i call in they told me the battery on the car was wrong and not properly fitted, the battery came with the car and it was working fine with it, i was confused. They swing the battery trying to get it started until the battery was finished and the car couldn’t start at all . They fitted a new battery and i was happy to pay for the invoice. Two weeks later when I was going to collect the car, i was told the car couldn’t start with the new battery, and they will further check car. There was some thing wrong with the fuel pump and it had to be replaced. The car is still on warranty, so the warranty approved for pump replacement. After pump replacement the car was working fine, now they are invoicing me for battery replacement, which i am not willing to pay because they swang the car until battery was finished and the problem was not with the battery but the pump. When the car came in, they were supposed to diagnose the car and find the root cause not assume that battery is the problem. They kept my car for full 3weeks and now one of their employees is harassing me on email to pay for battery invoice :(