To fix that error you normally either need to repair your Google Contacts in eM Client which clears the local contacts cache and then resyncs your online contacts to eM Client again.
Alternatively if repairing your Google contacts still doesn’t fix it, then suggest to next “remove and readd your Gmail account” via “Menu / Accounts” using the automatic account wizard.
If you do remove and readd your account, make a manual backup first via “Menu / Backup” incase you need to restore for any reason. You can see when the backup is complete in Show Operations via clicking the drop-down on the right of Refresh.