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This feature is part of integration with custom fields (Issue Checklist saves its content to Jira custom fields and next Jira adds entries in history, notification, etc.).
If you don't like notifications, you can either:
- vote the following Atlassian ticket so we can tell Jira to skip adding entries notification and history entries: https://ecosystem.atlassian.net/browse/ACJIRA-2077
- disable custom field integration on the Global Settings page
- in Activity Stream, filter out entries added by a user
- addon_com.gebsun.plugins.jira.issuechecklist (Pro version)
- addon_com.herocoders.plugins.jira.issuechecklist-free (Free version)
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