Your bullet point has no connection to green cards. GCC=Gulf Cooperation Council, which consists of Saudi, Bahrain, Kuwait, UAE, Qatar, and Oman. Assuming this is what you are referring to (and not what you posted above):
If this is your first time entering Saudi Arabia using a visa based on your Schengen, UK, or US visa/residency permit, please ensure your Schengen, UK, or US visa/residency permit is still valid.
Well your extension letter is proof your residency is still valid, so you should be fine.