This question is difficult because you have to select a right answer by meaning not by grammars only.
The modern rise of mobile, social, and location-based technologies has allowed humans to become
more tech-savvy now than at any time in their history.
(A) more tech-savvy now than at any time in their
Wrong. Correct grammar but wrong meaning.
A compares SAME object in different time frames. A seems to convey a meaning that technology has made people now more tech-savvy than themselves in the past. It's totally wrong. The intended meaning is that people now are more tech-savvy than people in the past (
different objects).
(B) more tech-savvy than they were at any time in their
Wrong. Same problem as in A.
B compares SAME object but in different time frames. It's not intended meaning. See explanation above.
(C) more tech-savvy than those at any other time in
Correct. C compares two DIFFERENT objects - people now and people in the past.
(D) more tech-savvy than those at any other time in their
Wrong. The main problem is "their". D seems to convey an idea that group A (now) is more tech-savvy than
group B at anytime
in group B's history. Wrong meaning. The intended meaning is "human's history in general".
(E) more tech-savvy now than at any time in
Wrong. Same problem as in A an B. E has correct grammar but wrong meaning.
E compares SAME object in different time frames. It's not intended meaning.
Hope it clears your doubt.