Appointment reminders are part of treatment, so you can send reminders without an authorization. While sending text message reminder, you should use common sense. Sending appointment reminder through SMS can't 100% HIPPA compliance, since the message will be stored or archived at some point either with us or carrier.
We can delete the messages from our servers with your permission, but we can't control upstream carriers. So you need to use common sense and customize your reminders as per your practice. For a pediatric or dental practice sending reminders to parents or patient, it may be just fine to include the time, date, location and provider in the appointment reminder. However when privacy concerns are extremely high, such as with an AIDS clinic, you may want to avoid using doctor's name, location and patient name in your text message and it can formatted as, "You have an appointment coming up on {date}."