The e-mails sent to users after they successfully submit an unsubscription request are based on the Newsletters - Unsubscription request e-mail template, which can be edited in Site Manager/CMS Desk -> Administration -> E-mail templates.
The unsubscription link in the sent e-mail will only be valid for the amount of hours specified in the Site Manager -> Settings -> On-line marketing -> Newsletters -> Double-opt in interval setting (12 hours by default).
Help URL: http://devnet.kentico.com/docs/webparts/index.html?UnsubscriptionRequest_overview.htm