Is there proof that backreaction of inhomogeneities is irrelevant in cosmology?

In a number of papers Green and Wald argue that the standard FLRW model approximates our Universe extremely well on all scales, except in the immediate vicinity of very strong eld astrophysical objects. In particular, they argue that the effect of inhomogeneities on average properties of the Universe (backreaction) is irrelevant. We show that their claims are not valid. Specically, we demonstrate, referring to their recent review paper, that (i) their two{dimensional example used to illustrate the tting problem differs from the actual problem in important respects, and it assumes what is to be proven; (ii) the proof of the trace{free property of backreaction is unphysical and the theorem about it is mathematically awed; (iii) the scheme that underlies the trace{free theorem does not involve averaging and therefore does not capture crucial non{local effects; (iv) their arguments are to a large extent coordinate{ dependent, and (v) many of their criticisms of backreaction frameworks do not apply to the published denitions of these frameworks.