Hi Kelle,
Making an email invite survey anonymous is technically speaking, impossible. With enough digging you will always be able to see who submitted a particular survey using the email invite tool.
If you go to the email invite tab, and click the invite that you sent out, then under “summary info” select “Link starts a completely new survey” which will partially remove the tracking of a respondent. If you have already gone under advanced options and chosen to make it anonymous, then these two features combined are the best solution possible for making an email invite survey anonymous.
Hope this helps!
Dane