new belt would you pay or not

we fitted a new belt to a wf series hotpoint aprox 6 months ago cust rang at the begining of december reporting that the machine wasnt pumping out i attended the call myself and diagnosed a blocked filter i was unwilling to complete the repair as only the young daughter was at home and she had no money to pay me i advised that if she rang we would be able to call the next day (a saturday)to complete the repair . The customer rang the next morning complaining that we had called and not repaired the machine, after we explained why ,we arranged to call to repair machine that day ,the cust was demanding a time but we stated that we were actualy full for the day but we would squeeze her in and she would have to bare with us ,my colegue arrived approx 2 hrs later was let in by the same daughter and set about removing the filter only to find it empty. At the same time our office received a call cancelling the call as she had managed to get another company to repair it sooner 👿 our engineer left slightly annoyed . A week went by when we received a call from the same customer stating that the drum wasnt turning we advised her to contact the last company who had repaired it .The customer rang the next day stating that the belt has snapped and it was under warranty and we would have to repair it free of charge :rolls: we explained although not impossible it was highly unlikely that the belt snapped it was more likely to have burnt through due to items being trapped in the drum (the reason we changed it in the first place )and we do not cover belts under a warranty for that reason , now after a long argument, a couple of letters received and replied to we now have trading standards ringing i presume for our version of events but as i use xmas as the time when i have a long break i have not yet spoken to them and they are ringing back next week. Just wanted a few opinions really as to how other people out there would have approached this .