From a strict grammatical perspective, "had dedicated" is correct, since the continuing action of "dedicating" (i.e. devoting a significant amount of time and effort to something) has come to an end with the doctor's death.
For example, consider a more definite completed action in the past, e.g. The late Dr. Francis was a compassionate doctor who had studied in London before joining the Hospital.
However, when the action is not as specific, not as far in the past, and more of a property of the person being described, the construction with "had" is awkward, e.g. The late Dr. Francis was a compassionate doctor who loved his family as much as his work.
Something that a person IS survives their death. Something they have DONE must be situated correctly in time.
For many readers, "dedicated" probably falls into a grey area. If you read the word and visualize the concrete actions, you'll probably lean towards using "had dedicated". If you see it as an essence of the man himself, you'll probably find that "dedicated" by itself is more natural. It's not really a fair question for an exam.