Do I have to pay Quest Diagnostic Lab in advance for my lab services? They asked me to pay $40 or give them my credit card for billing.

No, you do not have to pay the $40 or give them your credit card. The money or credit card is asked for up front, but is not necessary to have the services. Once the EOB (Explanation of Benefits) is processed, Quest will invoice you for the co-payment you owe. If you did overpay them at the time of service, you should receive a refund from Quest Diagnostic.