The correct option is
B has arrived
The present perfect tense is used to describe something that happened in the past, but the exact time it happened is not important. It has a relationship with the present.
Have/has + past participle makes the present perfect.
In this sentence, it is already given that we would be using present perfect tense. Now since, the whole sentence is in the third person, we would be using "has" and not "have".
("have" is used in case of first and second person framed sentences.)
so the sentence comes as, "The letter has"
Now, for the past participle, it the form of a verb, typically ending in -ed in English, which is used in forming perfect and passive tenses and sometimes as an adjective. In this case the past becomes, "arrived" and not "arriving". This eliminates Option C and D.
In Option B, "had" has been used which is wrong.
Option A is correct