We'll just send a email blast.
In our privacy policy page we did mention that third parties may have access to your information.
I'm not sure if that means they can also receive e-mails from those 3rd party.
You may need to discuss with a lawyer, since with GDPR and maybe other laws, lately you have a good chance to get a fine much more consistent than what you'd get from anybody "renting" those e-mails.