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This feature is part of integration with custom fields (Issue Checklist saves its content to Jira custom fields).
If you don't like this featurenotifications, you can easily disable it can either:
- vote the following Atlassian ticket so we can skip adding entries notification 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) or `addon_com.herocoders.plugins.jira.issuechecklist-free` (Free version)