This is a fairly simple question.
Lets go over the tested concepts quickly-
1) ModifierThe sentence starts with the modifier- Performing a risky maneuver that required precision flying
This is an action verb-ing modifier that should modify both the clause following it and make sense with both the subject and the verb.
What this means is the subject can't be the satellite as it did not perform the action of performing a risky maneuver, the action logically makes sense with the astronauts as the subject.
2) IdiomThe idiomatic usage of not only is- not only X but also Y
The original sentence does not contain but also which is essential for the correct idiomatic usage.
3) ParallelismThe astronauts did two actions- they retrieved the satellite and simultaneously avoided the telescope
To make this list of action parallel we need to make both the actions to be in the same tense.
Based on these 3 concepts, we can see that the only
correct sentence is E.
Sentence A has idiom and parallelism error.
Sentence B corrects the idiom and parallelism error but introduces modifier error.
Sentence C also has modifier error.
Sentence D has parallelism error.