The right answer is D.Split #1: Their vs its
The logical referent for the pronoun their/its is the Hubble Engineering Team, which is singular. The plural pronoun their is inappropriate. We can eliminate A and B.
Split #2: is vs had been vs has been
The subject of the main clause is the Hubble Engineering Team with the verb requested, which is in simple past tense. For the verb tense to be simple present tense is, then the verb for the main clause should have been in the simple present tense requests. But since the main verb tense in the main clause is simple past, the past perfect is more appropriate. We can eliminate C based on this split. The main clause suggests an action that is completed, hence there is no justification for the use of the present perfect tense.
Split #3: recent vs recently.
recent is an adjective and in the context of this sentence modifies failure. Recently is an adverb that can only modify the adjective unexpected and this is not intended. There is no reason to use an adverb form recently when an adjective recent can appropriately modify failure. We can eliminate E and keep D as the best answer.
Reporting that one of their more debilitating setbacks has been the recent unexpected failure of the Space Telescope Imaging Spectrograph, the Hubble engineering team requested additional funding to develop more reliable instruments.
(A)
their more debilitating setbacks
has been the
recent(B)
their more debilitating setbacks has been the
recently(C)
its more debilitating setbacks
is the
recent(D)
its more debilitating setbacks
had been the
recent(E)
its more debilitating setbacks
had been the
recently