Explanation

Fullerenes are made in the lab under certain temp & pressure conditions (i.e to make them, we need certain conditions say temp of 500 degrees C and pressure of 100 pascals).

Now fullerenes have been discovered naturally. So if we can find the time when these fullerenes were formed (say 2 million years ago), we can say something about the temp and pressure of Earth's crust at that place where fullerenes are found (that 2 million years ago, at the fissures, the temp was probably 500 degrees C and pressure was 100 pascal. This gives us some information about the temp and pressure of Earth's crust).

That is what the argument is saying. That we have better data available to evaluate hypotheses about the Earth's crust at that time.

We need to weaken this conclusion.

(A) Confirming that the shungite genuinely contained fullerenes took careful experimentation.
Irrelevant how it was found. They have found it.

(B) Some fullerenes have also been found on the remains of a small meteorite that collided with a spacecraft.
Irrelevant. The same conditions could have prevailed on the meteorite too. Doesn't weaken our argument.

(C) The mineral shungite itself contains large amounts of carbon, from which the fullerenes apparently formed.
This doesn't weaken our argument. The temp and pressure required in the lab can give us clues about Earth's crust.

(D) The naturally occurring fullerenes are arranged in a previously unknown crystalline structure.
Correct. This weakens our argument. The structure of the lab fullerenes is different from the structure of the natural fullerenes. The conditions required to make the two types of fullerenes could be very very different then. So lab fullerene conditions are unlikely to help us figure out condition of Earth's crust. For example, both graphite & diamond are made from carbon. But their structures are different. Very diff conditions lead tot he formation of one or the other.

(E) Shungite itself is formed only under distinctive conditions

Irrelevant

Answer (D)