I’ve never seen a server arbitrarily remove /redirect away from specific GET parameters. mod_security can filter for those, but I’ve only ever seen those end in a server error, not a rewritten/redirected URL. While it’s ideal if your server supports URL segments fully, it’s not a requirement. It is a red flag, but only a small one.
Can you confirm that cutting and pasting with that URL “lands” you on the same URL but without
group_id? And that you don’t have any other issues in your control panel? If that’s the case, you should be able to create an isolation test to show to the host. An external PHP file, with:
if ( ! empty($_GET))
Echo "GET is empty";
Access it via https://example.com/test.php?foo=bar&group_id=2&bat=bag, which would demonstrate the problem outside of ExpressionEngine. That is of course only if you see the same behavior in the ExpressionEngine control panel, and aren’t having any other issues.