This is registered as a custom task rather than hook-based per addon. That should not be the case. I'm going to modify it to be addon hook based.

Automated response: Deleting the Health Check addon leaves a task in Admin CP

The health check task was being installed as a custom task rather than being a hook on the main_staff_checklist block. Therefore, the task would remain even after uninstalling health check.

This hotfix fixes that. Note that if the custom task exists, it will still need to be manually deleted from the checklist. But this adds a health check specific task linked to the addon.

A hotfix (a TAR of files to upload) has been uploaded to this issue. Only apply this hotfix if you absolutely need it and cannot wait until the next release of Composr (releases are more reliable and strictly tested). As of Composr version 11, the recommended way to apply a hotfix is by following the same steps as an upgrade (https://baseurl/upgrader.php, use the hotfix on the step “Transfer across new/updated files”). The upgrader will automatically skip files belonging to addons you do not have installed or that are newer on disk than in the hotfix. Otherwise, you can manually extract and replace these files (do not replace if your on-disk file is newer than the one in the hotfix). Always take backups of your site or at least files you are replacing before applying a hotfix. Not sure how to extract TAR files to your Windows computer? Try 7-zip (http://www.7-zip.org/).

Apparently the actual hook did not get pushed into the hotfix. You may need to check for the commit after the one linked above.