Can the credit card of China Construction Bank change its password through SMS?

No, it's not safe to change it with a mobile phone.

If you remember the previous password, you can modify it directly through the ATM of CCB, which is the most convenient. If you can't remember the previous password, you need to call the customer service hotline, or you can bring your ID card and card directly to the financial counter of the outlet to make changes. If you need to change the telephone banking password, you can only change it through the customer service hotline.