Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
The description goes well past the annotations, which only declare readOnly/idempotent/non-destructive. It explains the whole flow (parent opens the link and hands it to the student, results appear on SATCoach's site and arrive by email) and, critically, that "Nothing about the check or its results comes back to you" — the single most important behavioral fact for an agent deciding how to frame this to a family.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.