Do gravitational waves lose energy through interaction with i.e. matter or magnetic fields? Gravitational waves dilute while traversing space like any other radiation, and their amplitudes are proportional to r-2, that's a basic. But do they lose energy while traversing through matter or something else (i.e. space with magnetic fields, or whatever), too, by interaction with it ?
(The question "Where does gravitational waves' energy go?" doesn't focus on traversing matter of fields)
 A: Your question is very original, and I have never seen it addressed, so here are my own hastily prepared thoughts on the matter.  Caveat lector. 
You can gain some insight into the fate of gravitational waves by pursuing the analogy with electromagnetic waves, which get both scattered and absorbed.  EM waves get scattered by matter that responds to the electric field -- free charges, good conductors, or polarizable objects.  They can also get absorbed when dissipative processes are at work -- in imperfect conductors, or dielectrics with lagging response.  
Dissipative processes generally involve reequilibration, which can be either fast or slow.  In imperfect conductors, electrons accelerated by the field ultimately lose their momentum by collisions with positive ions.  In water, it takes roughly 20 ps for the polar molecules to reorient.  
When GR waves passes through a galaxy, the tidal forces will deform orbits and objects, and the waves will surely undergo some scattering.  But what of dissipation?  Near misses by stars and lesser objects redistribute momentum slowly, but the tidal disturbance may either be brief (if the wave comes from a catastrophic collision) or periodic (if radiated by a binary star system).  MHD dissipation within individual stars acts faster.  
As for magnetic fields in empty space, they would push back when squeezed by tidal forces, much as in MHD, so scattering is to be expected, but not absorption, for lack of dissipative processes.  
