This is because you are using Appointment Request Forms. This can be switched off in User Management Portal
When a patient clicks on an appointment booking link and there are no appointments left, they will see one of two things:
1. A default message explaining that there are no more appointments available and to contact the practice to make an appointment
2. The ability to submit and Appointment Request Form.
If your practice admin users have included an email address in the Appointment Request Forms section of the User Management Portal, patients will have the ability to send a request form to the email address that has been entered.
If you would like to stop this, and remove the ability for patients to submit requests to the practice email, simply remove the email address in the Appointment Request Forms section of the User Management Portal (see below).