Looking at the paper abstract it seems like an interesting technical exercise to learn from. One of the challenges with ascribing a tiny mass to the graviton is

Looking at the paper abstract it seems like an interesting technical exercise to learn from. One of the challenges with ascribing a tiny mass to the graviton is that all the nice properties (symmetries) we’re used to in the context will go out of the window. Maybe there are some intricate tricks which will unlock most of the value of having those exact symmetries. Further, if the graviton has a mass, then it would be very surprising/difficult to reconcile it with observational evidence. Forces mediated by massive force carriers have an exponentially decaying effect over distance (dominating over the inverse-square effect). That would seriously clash with our understanding of the action of gravity over large/cosmological distances.