Final answer:
The thymus is the lymphatic structure that cannot be palpated, as it is located deep within the chest cavity, unlike the other structures which are more superficial.
Step-by-step explanation:
The lymphatic structure that is impossible to palpate among the options given is the thymus. When comparing the structures like lymph nodes, tonsils, thymus, and spleen, the thymus is located deep within the chest cavity, above the heart and behind the sternum, which makes it inaccessible to touch through the skin. On the other hand, lymph nodes can be felt in areas where they are close to the skin, such as the neck, armpits, or groin. Tonsils are visible at the back of the throat. The spleen can sometimes be palpable if it is enlarged, such as in certain diseases, but the thymus remains impalpable.