"Customers can also easily opt-out of having their voice recordings included in the fraction of 1% of voice recordings that get reviewed. For more information related to Alexa and Privacy please see here."
To delete Alexa conversations, visit the Alexa app, go to Settings > Alexa Privacy > Manage Your Alexa Data. From here, select Choose How Long to Save Recordings > Don't Save Recordings > Confirm. Next, scroll down to Help Improve Alexa, and switch the Use of Voice Recordings to off.