The 3+1 dimensional spacetime is not embedded in a higher dimensional space [1]. If there are additional dimensions, they have to be "rolled up" and tiny.
I wish I could read a paper like this one! My takeaway is that is no leak, but this doesn't prove that there are not higher dimensions in space, just that the gravitational waves can't get through it (if exists).
[1] http://iopscience.iop.org/article/10.1088/1475-7516/2018/07/...