Click here if you are concerned about your personal information and learn what you can do about it. Find out where the commands you have given are stored during interactions with the Google Assistant software and Home devices. All these elements of personal data are linked to your Google Account profile and you can  learn how to access them and remove part, or all, of them as required.

Click here for a detailed CNET article called "Google Assistant will remember everything, forever, unless you tell it when to stop". If you read down the article a bit you will find  what is held and how to delete it in different ways.

Unfortunately the Google Assistant may pick up parts of a conversation that you didn't want it to. Sometimes you, or the radio / TV, may say something that sounds like your trigger word and the Google Assistant will jump into action by mistake. Whatever the case simply say, "Hey Google, That wasn’t for you." and the last thing it heard {and processed} will be deleted.

A couple of similar commands that are handy to know are "Hey Google, Delete my last conversation" or "Hey Google, Delete today's activity."