Many people have requested that this plugin doesn't spam the jira comments section (e.g. JENKINS-12605). JIRA plugins such as marvalution may work for in-house jira instances, but not hosted or on-demand instances.

Instead of using comments, could the new jira remote issue links be created instead. These will be shown separately from the comments and could link directly to the jenkins builds.
https://developer.atlassian.com/display/JIRADEV/Fields+in+Remote+Issue+Links