To my limited knowledge, the last release of ZoneAlarm (free firewall only) compatible with Windows 9x was version 6.1.744.001 (approximately 10.0MB). My zlsSetup_6.1.744.001.exe installed on 98SE is time stamped 16th March 2006. There may be a later compatible version, I've not checked.
Physically disconnect machine from the network/Internet.
Uninstall ZoneAlarm.
Restart machine and install ZoneAlarm version compatible with 9x.
1. Type some name or leave at default. Skip Please type your email address (leave blank). Uncheck I want to register ZoneAlarm so I can download updates. Uncheck Inform me about important product and security news.
2. Click Next and check Accept.
3. Click Install. There is a slightly disconcerting delay.
4. There is no need to respond to any of the 4 survey questions, so just click Finish.
5. Yes, you want to start ZoneAlarm now.
6. Check Select ZoneAlarm (Award-winning firewall only).
7. Click Next. Click Finish. Click Finish. Click Done. Click OK to restart your computer.
Set tvdumpflags=8 should flash past during restart.
1. The License Wizard appears. Click No, Thank You.
2. Overview/Preferences/Check for Updates: Manually. Disregard the dire Warning! and click OK.
3. Close the ZoneAlarm window. Check Don't show this message again and click OK.
Reconnect the machine to the network/Internet. ZoneAlarm should now no longer check for updates. I was unable to replicate the problem as described. I tried installing the latest version of ZoneAlarm Suite (with the Conficker fix) on Windows 98SE and received the wrong Windows version message but then had no problem reverting to the original 9x version. I hope that setting Preferences/Check for Updates to Manually will solve the problem. I have suggested this complete uninstall/reinstall procedure because the OP said they were stuck with an uncloseable update window on each restart and it seemed best to start with a clean slate; it may not be necessary if they can just turn off Automatic Updates in the main ZoneAlarm preferences window and then restart.
My 98SE install of ZoneAlarm passes all the Gibson Research Corporation ShieldsUP!! tests (when both Internet and Trusted Zone sliders are set to High), so stick with it if possible.