+1 for D.

A. letting it go where circumstances are auspicious to do it in the future

B. letting them go where circumstances are auspicious to do so in the future

C. letting them go when circumstances are auspicious to do it in the future

D. letting it go when circumstances are auspicious to do so in the future --> Correct, 'art - it (singular)', 'to do so' over 'to do it'

E. letting it go when circumstances are auspicious to do it in the future

Hence, D.
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A. letting it go (where) circumstances are auspicious to do (it) in the future

B. letting (them) go (where) circumstances are auspicious to do so in the future

C. letting (them) go when circumstances are auspicious to do( it )in the future

D. letting it go when circumstances are auspicious to do so in the future - correct

E. letting it go when circumstances are auspicious to do (it)in the future

So, instead of it, should be used to represent an action.
When should be used to modify time.

Posted from my mobile device

IMO - D is the answer.

A. letting it go "where" circumstances are auspicious to do "it" in the future - Incorrect - It has no antecedent. Also, where is incorrectly used here. Where refers to place.

B. letting "them" go "where" circumstances are auspicious to do so in the future - Incorrect - Them is wrong here. It should be used.

C. letting "them" go when circumstances are auspicious to do "it" in the future - Incorrect - Them is wrong here. It should be used, also it is incorrect here.

D. letting it go when circumstances are auspicious to do so in the future - Correct

E. letting it go when circumstances are auspicious to do 'it' in the future - Incorrect - It is wrong here.

Posted from my mobile device

A. letting it go where circumstances are auspicious to do it in the future --Do what in the future ?

B. letting them go where circumstances are auspicious to do so in the future -- usage of them is incorrect .

C. letting them go when circumstances are auspicious to do it in the future --same as A and the usage of them

D. letting it go when circumstances are auspicious to do so in the future --correct !!

E. letting it go when circumstances are auspicious to do it in the future -- same as A !!

OE

The original sentence uses the unidiomatic phrase "to do it" to refer to the action of "letting the art go." The proper idiom is "to do so." Additionally, the word "where," which can be used to describe only physical locations, is incorrectly used to describe a time ("in the future"); the word "when" should be used instead.

(A) This choice is incorrect as it repeats the original sentence.

(B) This choice correctly uses the idiomatic phrase "to do so" to refer to the action of "letting the art go." However, it incorrectly uses the plural pronoun "them" to refer to the singular noun "art." Moreover, the word "where," which can be used to describe only physical locations, is incorrectly used to describe a time ("in the future"); the word "when" should be used instead.

(C) This choice correctly employs the word "when" to describe a time "in the future." However, it incorrectly uses the plural pronoun "them" to refer to the singular noun "art." Moreover, the phrase "to do it" is unidiomatic; "to do so" is required instead.

(D) CORRECT. This choice correctly uses the idiomatic phrase "to do so" to refer to the action of "letting the art go." Additionally, the word "when" is properly used to describe a time "in the future."

(E) This choice correctly uses the word "when" to describe a time "in the future." However, the phrase "to do it" is unidiomatic; "to do so" is required instead.