If you use Chrome you'll hopefully know there are settings that can control the information that it stores and syncs. I always turn off the offer to sync passwords - and also credit card details. But although you can stop syncing your credit card details, Chrome will still popup a message each time you enter a credit card number to ask if you want to save those details in the browser - and it doesn't provide an option to turn this off.
However, the following undocumented settings might be able to turn off the credit card details save prompt.
- Type chrome://flags into the address bar of the browser
- Search on the resulting page for "Google Payments card saving checkbox"
- Change the setting to Disabled
I am not sure that this works because I was still prompted to save when I put in a credit card number the other day.