Should I Dispute This Private Parking "ticket" With My Credit Card?

Let me start with this by saying while I don't enjoy paying for parking, I always do. If I see that I need to pay, I do. I'm a low risk person.

Two nights ago, I was going to pick up some food late at night, around 9 pm in my medium sized town, less than 50,000. It's in a parking lot that's almost always vacant, with no large signage in the parking lot. I was out of my car for about 10 minutes as the food wasn't ready, and as I returned, I saw a sticker on my window saying that I have been "taggd" or something like that. I look at the spot because I'm bewildered, and see that against the wall from my car, probably 8 feet in front, is a knocked over sign leaning against a wall, somewhat hidden by foliage. It was by a company named Taggr. They put some janky bike lock on your tire, one that you can easily drive off with, and threaten that it will damage your car if you leave it on (probably wouldn't). You scan a barcode, blah blah, and I'm shocked to see that it is a $99.18 "ticket," afterwards they tell you the code to their bike lock, where you then have to drop it off in their dropbox or else face another $75 charge. Again, it's a bike lock.

I'm furious. I look behind me and notice there there is a tinted mini-van parked a few spots away, I'm guessing the guy who did it. I start doing research, and see that they don't technically have any legal power. However, worried about risking taking the lock home and resulting in being accused of thievery, I didn't want to risk it. I try to find a way to dispute, and they have a text option, however the two options are something like "proof of payment for parking" and "didn't pay for parking." I click the latter, and it just says, "sorry you can't dispute." There is a phone number, but it is "only for payment." At a loss of what to do about an hour later, I decide to just pay it because I need to get home. I return the lock, and head home.

Once home, I do some more research. I read my city's code and try to find some state laws (Virginia). I find that there are several city violations regarding this, including the sign being knocked over, certain design flaws, etc etc. Not as much luck with the state laws. So, I decide to keep going. Luckily I took several crime scene photos after my horrific actions, including the knocked over sign and the low visibility, the lack of one large sign, and a couple of other photos. I crafted my email, laying out my issues, their code violations, and my plans to reach out to the city, and the local store (my town is very small business vibes - poor customer service is basically a death sentence for a business) if I'm not reimbursed.

Today, I receive a response saying that Taggr is simply the enforcer and that all of those issues are not their problem, and I should've disputed before paying (again, I couldn't). Therefore, there will be no reimbursement.

I personally find this quite ridiculous, as well as the fact that a don't have $100 lying around. I want to dispute it with my credit card, however I am worried about the following things:

1. Will my credit card dispute it
2. Can it hurt my credit score (I have a credit score over 750)
3. Can/or more so will they send me to collections, and if so is it a battle I will lose

I know many of you may tell me to just eat it, but besides the fact that I find this borderline illegal and upsetting, I don't have much money to pay for it. I'm a college student who works part time to support myself.

Any advice would be greatly appreciated - I also am sure I can call for long enough to find a customer service agent to talk to, but I'm hesitant as if I do dispute it, I don't want to have caused a scene for them to be more aggressive about.

TLDR - a private parking company gave me an unfair "ticket" and I'm curious about the ramifications of me disputing it with my credit card.