The blank screen issue occurs when the browser thinks it can't display the content of the file being requested. This is usually the case for many binary file types that aren't images/sounds/videos.
Version 0.52 of the mod-globus (RPM) or libapache2-mod-globus (DEB) package contain an updte to show a page with a download link when the request comes from an external link or from an auth redirect, so upgrading that package may fix your problem.
If the content of the file doesn't match what you expect, you might need to check that the path is correct and maybe look in /var/log/gridftp.log if there's an error.
If you are still having trouble, feel free to contact Globus support:
https://docs.globus.org/globus-connect-server/v5/#globus_support
Joe