@BVC Just go to nearest branch and don't tell them anything. Ask for Account Modification Form, where you can fill your new mobile number for change. Submit it.
Or go for re-kyc form, though there's no need for this, if you update through account modification form.
Either you choose, A/c Modification Form (recommended as u don't need to fill lengthy details) or Re-kyc Form.
P.S:
They are not able to do so. I am not sure whether they are not willing or not able to do.
@BVC Yes, it will, put/fill your CRN (Individual) & Credit Card Number and other necessary details there. You need to fill mobile number for updation there as well and required to sign there. You may be asked to provide an ID proof.
Make a call to CC and ask procedure need to be followed for updation, branch is denying. Or better to contact Social Media Team through Twitter/ Messenger, explain branch is not allowing to update. They will guide you or compell branch to update it.
@BVC In case if they will deny saying that your sign is not registered with us that's why can't proceed then ask to proceed with aadhar verification, (biometric verification).
If again, they will give some excuse then ask what is the procedure? Ask to give in writing that they can't update mentioning the same reason. You will be complaining to RBI BO.