Have you changed/introduced authentication on the proxy? I'm not familiar with GoToMyPC software, but user name "SYSTEM" could be an indication that it runs as a service on the client machine and does not support/not configured for proxy authentication. Best of all check GoToMyPC support forums, e.g. try Proxy Pop Up Issue | GoToMyPC Customer Community
I did work a problem last year involving NTLM authentication issues. In that case it was a matter of updating the installed software to the latest version.
Getting to that point proved to be a PITA. This involved many attempts of re-installing the various software components. But, I found that you can't really start from scratch without re-imaging the system, because Citrix does not provide a clean uninstall program. And, trying to manually uninstall them breaks Internet Explorer. And, that just boggles the mind. They must be replacing components of Internet Explorer, and sets my infosec hackles on fire.
I've worked in environments with Citrix products for about a decade now. I have found many of the products to be of poor quality and difficult to secure and support. My opinion of Citrix has been on a steady decline since I first encountered them, and that last encounter made this opinion much, much worse. I've worked with too many quality enterprise products, and I've seen nothing from Citrix to suggest that they will ever produce a truly supportable product.
So, I don't know if any of this helps, but you have my sympathies.