The clear link doesn’t show up on the sheet itself. On whatever page you have the main shortcode that shows all of your current sign-up sheets, if the current user has signed up for anything, there will be another table list below the list of sign-up sheets showing everything you have signed-up for, and that is where the clear links will be (if enabled).
My plugin needs to know which user it was who signed up in order to show them what they signed up for and provide clear links. So, the user needs to be logged in when they sign up for something. If they are not logged in, but they use the same email address to sign-up as is associated with their user account, then my plugin is smart enough to assign that sign-up to the user who has that email address. But, they still need to be signed into their user account to see the list and the clear links.