Final answer:
The nurse should document a score of 3 (Adequate) in the nutrition category of the Braden scale for a client who eats more than half of most meals but occasionally refuses a meal.
Step-by-step explanation:
The Braden scale assesses the risk of developing pressure injuries by evaluating multiple factors, including nutrition. For a client who eats more than half of most meals but occasionally refuses a meal, the nurse should document a score of 3 (Adequate) in the nutrition category of the Braden scale. This score reflects that the client's intake is likely sufficient most of the time but not optimal, considering the occasional refusal of a meal, which might signal a potential for nutritional risk if patterns change or appetite decreases further.