It isn't clear why the arXiv posting was delayed so long. But, the response is in line with previous discussions in Deur's papers.
We comment on the methods and the conclusion of Ref. , "Does gravitational confinement sustain flat galactic rotation curves without dark matter?" The article employs two methods to investigate whether non-perturbative corrections from General Relativity are important for galactic rotation curves, and concludes that they are not. This contradicts a series of articles [2-4] that had determined that such corrections are large. We comment here that Ref.  use approximations known to exclude the specific mechanism studied in [2-4] and therefore is not testing the finding of Refs. [2-4].
A. Deur, "Comment on "Does gravitational confinement sustain flat galactic rotation curves without dark matter?'' arXiv:2306.00992 (May 13, 2023).
The introduction ends by stating:
To reach the conclusion that FSI is important for galactic rotation curves, Refs. [2, 3] performed static lattice calculations of the GR potential, and Ref.  computed that potential within a lensing model based on mean-field technique. The approximations of the former and the modeling of the latter break some of the tenets of GR. In contrast, the authors of  strive to be analytical and to preserve GR’s basic principles. Consequently, they employ different methods from Refs. [2, 3] and Ref. , whose results they could not reproduce. This lead the authors of  to refute the validity of [2–4, 7–11] and the basic connection of GEFC to GR.
In what follows, we expand (Section II) on why perturbative methods like the one used in  miss the non-perturbative effects of FSI of GR. Next, (Section III) we discuss the lensing-based model initially developed in  and signals two reasons why the calculation in Ref.  miss the FSI effects. Then, (Section IV) we argue that GEFC is in fact based on GR. We then summarize and conclude.
The conclusion states:
Disproving the non-perturbative, non-analytical results cannot be done by using the perturbative PPN framework as done in Ref. . That GEFC is unrelated to GR is rebutted by showing that GEFC’s approximations preserve the relevant features of its starting point, viz GR. This is achieved by applying GEFC’s method to known cases, which was done for 7 distinct potentials (free-field in 1, 2 and 3 dimensions, Yukawa force, leading order PPN, φ 4 theory, and QCD). Lets consider the following five facts: (i) FSI, a feature of GR, provides naturally and without invoking DM and DE a unified explanation of the phenomena otherwise requiring DM and DE when analyzed in frameworks where FSI is absent (Newtonian gravity) or cancels (cosmological principle); (ii) FSI makes predictions of novel phenomena that have been subsequently observed; (iii) Intriguing parallels exist between GR and QCD, both for the theories and the phenomena they control;<7> (iv) FSI provides an innate framework for observations not explained naturally in ΛCDM<8>; and (v) solving the equivalent QCD problem of determining the increase of the force magnitude due to FSI has been notoriously difficult and its resolution remains a leading problem in physics.
These facts suggest that, even if a calculation yields too small FSI, it more likely points to an insufficiency of the method, as the PPN in , rather than a failure of GEFC.
In the worst case scenario that approximations used in lead incorrectly to conclude that GR’s FSI are significant enough, then the facts (i-v) would be pointing to GEFC missing the right mechanism rather than being wrong. In fact, even if the proposed mechanism (FSI) has been misidentified, it would only put GEFC on the same footing as ΛCDM and alternatives, e.g., MOND, that are not supported by a verified theory. It would not affect GEFC’s demonstration that alternatives to DM/DE-based models are possible even in the era of precision cosmology: contrary to oft-stated, high-precision observations, e.g., that of the CMB, do not establish the existence of DM/DE.
Another example is the claim that the Bullet Cluster observation proves DM (this article is titled “A direct empirical proof of the existence of dark matter”). This is disproved by the fact that the observation is naturally expected by GEFC, immaterial to whether or not the FSI mechanism is relevant.
That the numerous parallels between cosmology and hadronic physics are purely fortuitous coincidences is unlikely, especially because of the similar theoretical structure of GR and QCD. It is injudicious to ignore these leads only because exact calculations are impossible and approximations can be contested. This is especially true in light of the issues presently faced by ΛCDM and the ability of GEFC to explain astronomical and cosmological observations.
As GEFC’s claims are outstanding and far-reaching, they must be rigorously scrutinized. This is what Ref.  undertook but with a method not adapted to the problem. The way forward is to test GEFC with numerical non-perturbative methods and remember that 50 years of trying to solve the similar, but simpler QCD problem has checked many methods.
Footnote 7: Specifically, these parallels are between (a) the GR Lagrangian, (b) the observations interpreted as evidence of dark matter, (c) those for dark energy, (d) the cosmic coincidence problem, (e) the Tully-Fisher relation, (f) galactic matter density profiles on the GR side, and (A) the QCD Lagrangian, (B) the magnitude of hadron masses, (C & D) the confinement of QCD forces in hadrons, (E) hadron’s Regge trajectories, (F) hadronic density profiles on the QCD side, respectively.
Footnote 8: Inter alia, the Tully-Fisher and RAR correlations, Renzo’s rule, cosmic coincidence, Hubble tension, dwarf galaxies overcounting, absence of direct detection of dark matter particle and absence of natural candidates within particle physics.