The car dealership can definitely see your credit card balances. This information is readily available on your credit report and upon checking your credit, the dealer will have access to all your credit accounts including your credit card accounts. In spite of this, there is no reason to worry about them having access to this information unless your credit card balances are affecting your credit score. Most dealers mainly focus on the credit score itself as opposed to specific details about your credit history and payment history.
If you are concerned that high credit card balances may affect your ability to lease a car, this could be a possibility. High credit card balances that are not paid off entirely when the payment is due, have a negative effect on your credit score. In fact, 30% of your FICO credit score – one of the most well known credit scores – is based upon the amounts you owe. If you have high credit card balances, it would be in your best interest to come up with a payment plan to reduce those balances as much as possible. Reducing the amounts you owe will definitely help boost your credit score.