What action by an assistive personnel delivering food trays requires the nurse's intervention?

The action that requires the nurse's intervention is providing a ham and cheese sandwich to a client who follows a kosher diet. Kosher dietary laws have specific restrictions about the types of food that can be consumed, including prohibitions on mixing meat and dairy products, and certain types of meats altogether. Therefore, serving a ham and cheese sandwich to someone who adheres to kosher dietary practices is not only inappropriate but also disrespectful of their cultural and dietary requirements.

In contrast, the other options present acceptable scenarios. Offering a vegetarian meal to a client with dietary restrictions aligns with their dietary needs, as vegetarian meals typically meet various dietary preferences. Providing a low-sodium meal to a hypertensive client is appropriate and beneficial in managing their condition. Lastly, delivering dessert to a diabetic client can be acceptable as long as it's within their dietary guidelines and parameters set by their healthcare provider.