I think "quite possibly" is wordy.

Thus A,B,C are out.

E uses incorrect "they" when the mountain frog is only singular.

Correct?

Option A.
' severe enough for the United States Fish and Wildlife Service quite possibly to list it'
This would have been a possible correct answer but the use of 'quite possibly' sounds incorrect and does not follow parallelism.
Option A is incorrect.

Option B.
'severe enough so that the United States Fish and Wildlife could well list them'
'them'????? 'mountain legged-frog' this is definitely a singular so it does mot need to attract plural pronoun
This makes this option incorrect.

Option C.
'severe enough for it quite possibly to be listed by the United States Fish and Wildlife Service'
The error in this option is quite similar to the one in Option A.
The use of 'quite possibly' sounds rather awkward,this makes the option incorrect.

Option D.
'so severe that the United States Fish and Wildlife Services could well list it'
Perfect Option.This is the most befitting option in all,because it truly explains the plans of the United states Fish and wildlife services in suitable manner,it doest not commits the error by the other options.The use of 'could well' shows possibility of listing the animal as endangered species.The use of 'it' shows we are talking about animal here.
THIS IS THE CORRECT OPTION.

OPtion E.
'so severe that they could well be listed by the United States Fish and Wildlife Services'
'they'??????? not for the endangered animal species.'it' would have been better.
This option is incorrect.