I am having this same behavior.
I just got the plug-in, so any other external gallery links were grandfathered in when I changed from my previous plug-in. I haven’t had a chance to check their behavior with Gallery Custom Links.
The one I’m struggling with is a new post, but I haven’t published the post yet because I’m hoping to have a fix before it goes live.
The links to external URLs work sometimes, but not others. I’ve tried deleting and reinstalling at both the gallery level and the individual image level. It seems random, but it seems to work better with my Amazon affiliate links, and less so with other links.
This is with WP version 5.3, Twenty Seventeen theme: https://www.edieeckman.com