Cosmic Graviton Background and Primordial Gravitational Waves

I understand inflation is thought to predict primordial gravitational waves although their strength is undetermined by the theory with some models of inflation predicting them to be strong and others so weak they can never be detected.
However , this paper claims that if we detect a background of cosmic gravitons then all models of inflation would be ruled out. https://arxiv.org/pdf/2208.14088.pdf
Can someone explain why primordial gravitational wave would not also make a cosmic graviton background? Why would detecting this background rue out inflation as a paradigm?

I have not yet read through the paper in detail, but I believe there might be an issue of terminology here. As I understand it, "primordial gravitational waves" means gravitational waves produced at the end of inflation due to tiny inhomogeneities in the reheating process (which would also cause fluctuations of other kinds). "Cosmic gravitons", OTOH, according to the paper, means gravitational fluctuations produced before inflation. The paper's basic argument seems to be that the latter kind of gravitational fluctuations would be smoothed by inflation the same way any other kind of fluctuations before inflation would be smoothed, so they would not be detectable once inflation had ended. But that's not the same thing as saying that there would be no fluctuations at all at the end of inflation; the end of inflation itself can produce fluctuations, as described above, and those could include gravitational waves.

thanks