Undersea mountains have gravity signatures very similar to overland mountains, even though the latter are significantly closer to space?

"Closeness to space" doesn't affect the gravitational force due to a particular piece of matter. Now, if water was as dense as rock, then undersea mountains wouldn't make such a difference to the gravitational field.

I'm trying to understand why you think "closeness to space" would be a factor. Maybe you are thinking that the seabed is going to be further from a detector than the terrain would be?

It is true that the further from the Earth the detector is, the smaller the anomaly will be.

Note that even hills are large enough to deflect the gravitational vector at the surface: https://en.wikipedia.org/wiki/Vertical_deflection

https://en.wikipedia.org/wiki/Gravity_anomaly