TraceWrangler does not use communication except for update checks.
Use System Proxy: TraceWrangler will try to determine your system proxy setting and use it to check for new versions
Use Proxy Server: if checked, it will allow setting a HTTP proxy server that will be used to check for new versions.
Check for update at program start: if checked, TraceWrangler will check for a new version at each start. You can configure it to skip the connectivity warning if no internet connection is available.