If it shortened all dimensions equally and at the same time everywhere, it would be difficult. But you're looking for a difference in shortening (or lengthening) of one arm of the detector (or the test masses in that arm) relative to the other.
It's a bit waves on the surface of a pond. Sometimes, they expand equally in all directions and form a circular pattern. Sometimes they are different in different directions. This can detect that difference.
Even if the wave is symmetric in all directions, the squeezing/stretching can reach the arms of the detector at different times, just like the points on a circular ripple will reach the short at different times.
Now, of course this is assuming that the waves travel at a certain finite speed (the speed of light as far as we know). If they traveled instantly so the change was everywhere all at once, things would be different.
But, we have pretty solid reasons to believe that they don't travel instantly: That Nobel prize in 1993, I mentioned for example. The amount of energy lost in gravity waves was that of a traveling wave of finite speed, not something that traveled instantly.