Earlier quoted context omitted.
In principle yes, gravitational waves dissipate energy into ordinary matter they pass through. However the coupling is extremely weak (that gravitational waves are so hard to detect is testament to this). In fact this weak coupling is what makes GWs so interesting for observational astronomy: They propagate from the source to our detectors virtually unchanged. (This is in contrast to EM radiation, which is very easy…
I would rate the weak coupling as a far second or third point of interest behind linear signal fall-off vs inverse square for most other kinds of signal such as electromagnetic waves. Gamma ray burst is twice as far away? It's four times dimmer. A thousand times as far? A million times more dim. Gravitational wave signal from is twice as far away? Makes it twice as hard to detect. A thousand times as far away? Only a…
The linear drop-off you're referring to is when we look at it in terms of field strength (in this case the spacetime strain). Since power is proportional to field squared, this implies a linear drop-off in the field. It just so happens that for GWs it's easier to detect the field, whereas for (most) EM radiation it's easier to detect power.
There are field-detection methods for EM radiation as well, which are useful for weak signals. Homodyne and heterodyne detection are good examples.