Do gravitational waves bounce the space upwards?

I will try my best to explain.

When I think about waves, I generally tend to first visualize a stable and flat two-dimensional surface, in position 0. When a normal sine wave travel through it, it moves the surface up and down, bouncing it to, say, +1 and -1. This is true for waves in water, sound waves and even waves in the electromagnetic field.

Is this true in regards gravitational waves? Or does it only bounces the space "down", between -1 and 0?

EDIT

To clarify a bit more: I want to know if gravitational waves generate a repelling force, even if it is microscopic and instant. This repelling force is what I mean by "upwards".

If there is no repelling force, then the answer to this question is "no", and the gravitational waves only work by slight increasing and decreasing the attractive force. And this is what I believe it is true.

If there is actually a frame of repelling force (in the negative mass fashion), then I believe this can be technically extrapolated (by using superposition of waves) to generate anti-gravity. (I don’t believe this is the case).