Comment by rtanaka

Yup, after you tokenize the card CVC (CVV2, CID, etc) is no longer needed. So even though it will change it won't affect the validity of the card since this sounds like a deal with the networks. Also, you're not allowed to store CVC any way so the system has to work without it. In some cases where fraud is suspected some processors can / may ask you to provide your current CVC before letting the charge go through.