You can add this script within the <BODY> tag to clear the user information as soon as they close the chat. 

Sample code:

window.fcWidget.user.clear().then(function() {
  console.log('User cleared');
  }, function() {
    console.log("User Not cleared");

However, this might increase the MUV number. This is because after clearing the user info when the same user visits the page again he is taken as a new customer and thereby increasing the count of unique visitors for the account. Customer may be charged extra for exceeding the MUV allowed for their plan.