All the changes to the checklist are tracked in the issue History tab and Notifications section, as presented below:

This feature is part of integration with custom fields (Issue Checklist saves its content to Jira custom fields).

If you don't like notifications, you 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)