The ingredients, the finished food, and cross-contact all matter more than a flour-free-sounding name.
Under FDA rules, a food labeled gluten-free cannot contain prohibited gluten-grain ingredients and any unavoidable gluten must be below 20 parts per million. A recipe that omits wheat flour alone does not prove its finished cookie meets that standard.
Our home kitchen handles wheat and other allergens. We share ingredient information and our cross-contact notice, but we do not present our kitchen as celiac-safe or promise a cross-contact-free cookie.