FreeBusy does not allow to change link of already created appointment type however you can clone an appointment type and change its link. This way you will be able to change link.

The best way to achieve this:

Step 1: Click on "Manage Appointments" on booking page to access appointment type for which you wish to change link.

Step 2: Click on three dot menus.

Step 3: Click on "Clone" to clone appointment type

Step 4: Change URL (You can keep appointment type name same).

Step 5: Clone Appointment Type