Hi Po,
While it is possible for contrib modules to provide mobile support, this feature is still fairly recent and the Checklist plugin does not yet provide that. I see a request for mobile support on the project's github page, but not development seems to have been done (yet).
I understand how it would be useful to have native support of this plugin in Moodle mobile, but this plugin is developed by a (volunteer, afaik) developer outside of Moodle HQ and is not part of Moodle core, so I'm not aware of the developer's current circumstances.
Mathieu