Change the way Constant Contact updates Preferences. You need to provide a way for contacts to click on "update preferences" without receiving another e-mail. Most other companies do this. Have a popup appear or automatically go to your website with verification from the initial users e-mail.
Have your programmers send a uniquely generated code for every email sent out by Constant Contact. When a user wants to update their preferences, send them to your website by autofilling the e-mail address and use the unique code plus the senders e-mail address to confirm their identity. (Making sure its not an unsubscribe from someone forwarding the email)
It is such bad practice to have a second e-mail sent that people need to click on in order to update their subscription preferences.
Also rename your option:
1. "Update Subcriptions" (Mange your e-mail lists that this sender has you on)
2. "Unsubscribe from all Future e-mails from ......" (You will not receive any more e-mails from this sender)