Yes, the syntax is correct in the sentence “When did they take back the unit?” Its syntax is actually as good as that of “When did they take the unit back?” I have not seen myself any grammar or syntax rule on which construction is better, but I can tell you that even if the second construction does sound better than the first in this particular case, the first construction is actually more flexible and versatile than the second.
Why do I say this?
In both sentence constructions, the object of the verb is the single-word noun “unit.” Both sentences work beautifully whether the noun-form “the unit” comes after the verb phrase “take back”—“take back the unit”—or is positioned in-between the verb phrase—“take the unit back.” However, you will discover that this syntax works only when the object of the verb is a single-word or at most a two-word noun. When that object is a multiword noun phrase—say, “the unit with the defective billing” (modified by a prepositional phrase), “the unit awaiting repairs” (modified by a participial phrase), or “the unit that was delivered yesterday” (modified by a “that”-clause)—the second construction that you favor can no longer work properly.
Look: “When did they take the unit with the defective billing back?” “When did they take the unit awaiting repairs back?” “When did they take the unit that was delivered yesterday back?” In all three cases, the syntax fails miserably; in fact, the modifier ends up as a misplaced modifier.
Now see what happens if we use the first construction: “When did they take back the unit with the defective billing?” “When did they take back the unit awaiting repairs?” “When did they take back the unit that was delivered yesterday?” Everything is in its proper place.
We can summarize the rule as follows: In sentence constructions using the “take back” verb phrase, when the object is a single-word or at most a two-word noun, you can sandwich the object of the verb between “take” and “back”; when the object is a multiword noun phrase, however, you need to position the noun phrase after the verb phrase “take back” to ensure proper syntax. (Of course, the same rule would apply to similar verb phrases like “bring back,” “send back,” “buy back,” and “call back.”)
This sounds like a very complicated rule for a simple question, but as in war, Jolie, doing the simplest could be the most difficult.
