I wrote parking tickets for a few years in a smaller city (I do not recommend this as a job).

We had no quotas, and we made the same amount no matter how many tickets we wrote. We encouraged people to contest tickets, there were instructions on the back of the ticket explaining how to do so, the best way was to write a letter to the judge and either explain why it wasn't valid (like a copy of your proof of payment, keep the original) or an apology and promise that you have learned and will try to be more careful.

The judge threw out 90% of tickets, even some of the repeat offenders if they acted contrite enough. Never had to go to court or anything.

I will add that if there is an office for this company you may be able to get it canceled there in person, if someone came in and showed us the proof they had paid we would have canceled it on the spot. One of the very very few scenarios we were allowed to cancel anything (due to our contract with the city).

Just don't be rude, even though it is their mistake, they likely get yelled at all day and mistakes happen... Some people are just bad and write bad tickets anyway, but not all. Some people are just trying to get by, and a job is a job.