The way that can be followed is not the true way. The path that can be seen in the grid is not the path to follow; instead, one must trace the missing path formed by completing the partial circles. (Another way of looking at this is as a hypercube, with sixteen vertices. The path presented is a Hamiltonian circuit, a closed loop that runs along the edges and goes through each vertex once and only once; the missing path is a "dual" Hamiltonian circuit, i.e. is also such a circuit. But you don't need to know any of this to solve the puzzle.)
If you trace the path in the correct direction (and there are only two possibilities, after all), you can read the pairs of lines as semaphore. Orienting each semaphore signal so that you read it as being upright as you approach it, and treating the circles as spaces, you get the message "REMOVE THE BLUE ", which is the answer. (Depending on where you start, but if you somehow got "UE REMOVE THE BL," and couldn't get the answer from that, you're on your own.)
For the sake of ultra-clarity, a table. The first row is the unoriented semaphore code; the second, the orientation; third, the oriented semaphore code; fourth, decoded letter. (And similarly for the second half of the message in rows 5-8.)
