If the Save local checklist items to Jira custom fields global setting is enabled, then Jira will track all changes to the checklist in the issue History tab and Notifications section:
There is currently no way to disable notifications in the Jira notifications panel. Please vote for these Atlassian tickets to allow the option to bypass notification when an issue is updated:
In the 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)
Users might receive email notifications of issue updates in accordance with the project’s notification scheme and their personal settings. If you want to leave integration with custom fields enabled, but don’t want Jira to send a notification whenever a checklist item is checked/changed, please either:
modify the notification scheme for a project in Jira
filter out emails using the app name
If the Send email notifications for user mentions global setting is enabled, then Issue Checklist will send an email to users who are mentioned in checklists. Currently, there is no way for individual users to unsubscribe from these emails.