The Postal Code dataset in Google Earth Pro appears to be somewhat out of date in certain areas, and there isn't a way to extract the data from Earth's built-in layers, so I would suggest going to the source for this data.
Searching data.gov for "postal code" brings up many datasets for different geographies, and time periods. I suggest looking through there to find what you need.
Note that, if my admittedly limited understanding is correct, post codes or zip codes are not originally polygon/boundary data. Apparently the Postal Service defines zip codes by the street and range of address numbers (which makes sense for how they use them to deliver mail), so they're really a set of linear features. Anywhere that you see post code boundaries or polygons, most likely someone has tried to estimate where the divisions lie between the streets. This is usually along property lines, but often is based on various assumptions.