this should be (d).

first off, "make do" is an idiomatic expression meaning, roughly, "get the job done" or "accomplish some planned goal". so that's fine, the above guest poster's assertion to the contrary notwithstanding.

(a) and (b) are gone because "it" doesn't have an antecedent.
(e) is gone because "settlers' homes" is the subject, creating the absurd meaning that the homes themselves "made do" -- i.e., that the homes built themselves.

(d) is better than (c) for the following reasons:
* "making them" would be wholly redundant, because we just got done saying "to build their homes". if this were the intended meaning, we'd just write "...used mud and grass to build their homes, without timber and nails". on the other hand, "making do" (which, as noted above, is an acceptable idiom) is acceptable as a modifier because it doesn't restate anything from the main clause.
* "while not having" is way, way inferior to "without". in fact, if you've seen enough official problems, you'll eliminate wordy constructions like this on sight; they're common, and they're basically never correct (especially when they're alongside much more compact constructions, such as "without", in the answer choices).