You can allow instructors / teachers to drop students and not allow the instructor to affect the invoice.
How? Go to Configure | User Access and select your instructor / teacher profile. Then click the following options:
1. Drop Student = Yes (checked)
2. Hide Financial Data = Yes (checked)
If you do both of those, the teacher / instructor can drop a student from their roster and the only option they will see is to notify the student = yes/no. The invoice will remain unaffected and not changed.