If as it seems that you're modifying an existing mod, then you could do:
Open the mods .mod.zip file, navigate to the data_common/excel folder, then drag and drop your gameglobals.txt.cooked file. You may need to remove the gameglobals.txt file(alternatively you could directly modify that instead).
Confirm that you do want to insert the file, and then reinstall the mod.
Open Reanimator and confirm that your changes have been made, if not double check you did everything right. If you can see your changes, then run the game.
If you're not modifying an existing mod you could do:
Assuming you have Reanimator in it's own folder like:
Hellgate London/Reanimator/Reanimator.exe
Create data_common/excel folder in there like:
Hellgate London/Reanimator/data_common/excel
Also create data folder like:
Hellgate London/Reanimator/data
Copy gameglobals.txt.cooked into there
Hellgate London/Reanimator/data_common/excel/gameglobals.txt.cooked
Then run Hellpack.exe. It should be in the same folder as Reanimator.exe.
Look in Hellgate London/Reanimator/data, and you should see sp_hellgate_1337_1.5.0.idx, and sp_hellgate_1337_1.5.0.dat. Move those files into your Hellgate London/Data folder. If there are already files by that name, rename your newly made files.
Open Reanimator to check that the changes have been made, if you don't see them double check everything was done correctly. If you do see the changes, run the game.