We need to see the Notice to Keeper (NtK) you received, both sides.
Your Plan A is the first step. Get the Management company to call off their agents.
Personally, I would never consider purchasing or renting a property that is infested by an unregulated private parking firm. You will live to regret it and so will any visitors or delivery people and they may even blacklist your address.
If you do choose to ignore my advice, you should check any lease very carefully for whatever it says about parking. What it doesn’t say about parking is equally important.
Caveat emptor.