Tagged question and perfect tense

Solution 1:

Strictly speaking all the first three could be considered "valid" (although #2 would be a somewhat contrived context, and would require the final "tag question" to be reversed into "..., will you?").

So I'd say this "online grammar test" is very poor quality, purely on the grounds that there's no single correct answer. All we can say for sure is #4 is a no-hoper.

But let's face it — any half-alert native speaker wouldn't come out with that clumsy repetition of "back" either. If it makes OP feel any better, #3 is actually closest to the more natural phrasing...

You will [make sure you] put it back before the boss returns, won't you?

For what it's worth, there is a difference in some contexts (not this one) between using future perfect (will have done) and simple future (will do)...

When I leave the office I will enjoy/will have enjoyed a few hours of leisurely relaxation.