If you hit a parked car you have two options. You can turn this in to your insurance company and they will settle the damage with the other party for the repairs. However, depending upon the insurance company's rules, they could increase your auto insurance rates for this accident. You may elect to pay for the repairs out of your pocket. If you decide to do this, be sure you get a qualified estimate from the other party's repair shop. You don't want them to come back and ask for additional money for additional repairs. Once you and the other person agree to an amount, get a signed ststement from them agreeing that the amount you paid is the complete amount.
You should not have any issues as to being a reckless driver, even if you report the damage to your insurance company. The police will not be involved unless the other party calls them. You do need to make a decision about how you want to pay for the damages so you can get this resolved soon.