How to troubleshoot the issue related to not being able to See/Update the Global Variable (GV) in TEA UI even though the GV is present in project and the EAR used for deployment? 

For BE application deployments using TEA it's required to enable the checkbox "Service settable" for the GVs in studio project to be able to edit and update the Global variables in TEA. 

In TEA , The checkbox "Service settable" only will be used to determinse if the GVs are available for edit. GVs can only be updated when this flag is enabled. 
Note :The other flag (Deployment Settable) will be ignored and not used in BE-TEA. 

Please enable the checkbox "Service settable" in BE Studio and recreate the EAR and deploy in TEA and see if that helps.