Member awaiting confirmation

I have a member who has returned to an old email.  She had stopped using it 4 years ago and has been in the "awaiting confirmation" category since then.  She has just started using that email again and desires to be added back on our mailings but cannot find the original reconfirm email form 4 years ago.  We do not have html expertise so adding pop up or other online sign-up mechanisms are not options.  How does the "paper sign-up" form work ? How do I verify I have the party's permission to add them back in to receive active mailings?