My take is that if it’s a private parking company, and not an “old fashioned” legit parking ticket issued by “old fashioned” publicly-paid parking wardens, chances of it ending up in court are pretty much slim to zero.
I wouldn’t lose any sleep over, that’s for sure. Life’s too short (for me at least) to be worrying about these minor irritations.
I also reckon the thing that most people will feel threatened/bullied by (and therefore don’t bother contesting and just pay up for an easy life) is the potential outcome of non-payment of the fine itself. This is the main “bogeyman” threat used by these private companies telling folk they’ll get a “black mark” affecting their “credit score”, which I reckon must be a humongous chunk of the population these days, making it a highly effective modern-day weapon to get people to pay up, even when the circumstances of any fine are highly questionable.
If it’s a legit parking ticket, i.e. issued under a TRO or under Highway Code rules and not on some privately owned and managed land used for parking, then you can still contest it, but only if you can provide evidence to back yourself up. As it appears to be the case that your sil would find that a little more difficult (paid cash, no ticket retained as evidence) then it will be easier to just pay up and put it down to experience - and to remember to hang onto any physical tickets for a few weeks if parking in the same way in the future just in case