Today's technology allows manufacturers to make
small cars more fuel-efficient now than at any time in their production history.
Option Elimination -
(A) small cars more fuel-efficient now than at any time in their - "now" is redundant. "their" refers to "small cars" or "manufacturers"? Wrong.
(B) small cars that are more fuel-efficient than they were at any time in their lives. "They" refers to the same old cars, creating a ridiculous meaning. We need a demonstrative pronoun to create a copy of small cars.

. Moreover, we need "other" as we have "any," and that will include "today's" as well. So I'm afraid that's not right.
(C) small cars that are more fuel-efficient than those at any other time in - ok. "those" refers to small cars.
(D) more fuel-efficient small cars than those at any other time in their - "their" is ambiguous. Does "those" refer to "fuel-efficient small cars"? Are we comparing "fuel-efficient small cars now and fuel-efficient small cars in the past? Moreover, are we saying we are producing 100 blah blah than 10 in the past? Are we comparing the number of fuel-efficient small cars with those of fuel-efficient small cars or small cars in the past? This option seems like a mess.
(E) more fuel-efficient small cars now than at any time in - we need "other."