We currently include Jenkins outgoing proxy info in the support bundle - https://github.com/jenkinsci/support-core-plugin/blob/master/src/main/java/com/cloudbees/jenkins/support/impl/UpdateCenter.java#L75
I'm proposing we try detecting reverse proxies as well.
A simple (but not bulletproof) solution is to look for the presence of the X-Forwarded-For header in responses to the configured Jenkins URL.
This solution would work for non-anonymous proxy servers.
Anonymous proxy servers would not include this header (by design).
Misconfigured proxy servers would potentially also not include this header.