Hi @Al Doman ,
By researching, users are not supported to modify the GAL via Outlook client. Only administrators with permissions can use the Exchange Management Shell to create, modify, remove, and update GALs. Please refer to: Global address lists
About how to use the Exchange Management Shell to update/modify global address lists, please refer to this link: Procedures for address lists in Exchange Server
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The web-based EAC/ECP can also be used to manage Contacts in the GAL and Distribution Groups which contain those Contacts.