Answer and Explanation:
The limited narration in the third person has as main characteristic to allow us to know in a deep and very detailed way all the feelings, thoughts, fears, convictions and emotions of a character, similar to the narration in first person. The difference is that the first person narration is told by the character himself. This type of narration is unreliable, because the character can exaggerate facts, manipulate information and present bias whenever necessary and we readers will never know because we only know this character's point of view. The limited narration in the third person does not have this problem, because the narrator is reliable and shows everything in an impartial, complete and unhandled way.
This feature of the limited narration in the third person is very important in "After Twenty Years" because it allows us to get to know the characters as they really are and shows us the true thoughts that they have of each other after meeting after 20 years. We know what has changed in their view, how they interpret this friendship and this pact to meet. This generates surprise because we can discover pretenses and reactions totally unexpected and contradictory to what the character presents.