How can I allow an anonymous user to generate an email to themself?
Someone else may have a simpler answer, but here's how I would do it:


Install the extensions "CiviRules" and "Email API".
Create a group called "Requested Data Update Email".
Create an email template with whatever you want, including the checksum.
Create a rule that when someone is added to the new group, they receive the email you just created.
Create a profile (or a Caldera form, if you prefer) that requests email, and any other info you like.  Configure the profile so that submissions add the person to the new group.
Optionally, add a second action to your rule to remove the person from the group, depending on whether you want them to be able to request the email multiple times or not.