There would have to be code in Kibana that sends info to the parent page through post messaging. That isn't a built in feature, but there is a plugin that seems to offer that: https://github.com/bondib/kibana-iframe-communicator-plugin
See also Kibana Iframe Communicator
Note that Elastic team members can not officially support or endorse 3rd party plugins. We do not review the code for security vulnerabilities or anything like that.