Hi typically when the site continues to render what the plugin was doing it is due to a caching plugin that was present on the WordPress site itself. That usually would show up in the list of plugins in the plugin list. Additionally, some caching plugins install menus either in the menu area on the left side of your admin panel or may have a menu option withing the ‘settings’ menu. When/if you find something that looks like a caching plugin you would choose the clear/delete cache option.
As an aside, the reason why I’m quite sure that a caching plugin is in play is because once you uninstall the maintenance mode plugin, there is no code to generate that page anymore unless something else out there has retained what the page looks like.
Bob
P.S. If you can’t find the caching plugin, you may want to check with your provider if they have some other type of caching installed at the web server level.