  The Ultra-Diffuse galaxy NGC1052-DF2 has recently been under intense scrutiny
because from its kinematics it has revealed to be "extremely deficient" in dark
matter, if not lacking it at all. This claim has raised many questions and
solutions regarding the relationship between baryons and dark matter in
Ultra-Diffuse galaxies. But there seems to be a quite unanimous belief that, if
such very low dark matter content is confirmed and extended to other similar
galactic objects, it might be a deathblow to theories which modify and extend
General Relativity. Deficient dark matter galaxies thus represent a fertile
ground to test both standard dark matter and modified gravity theories. In this
work, we consider a specific Degenerate Higher-Order Scalar Tensor model to
study the velocity dispersion of ten compact globular clusters-like objects
associated with NGC1052-DF2 to infer the dynamical mass of the galaxy. Due to
the partial breaking of the corresponding screening mechanism, this model can
possibly have large cosmological scale effects influencing the dynamics of
smaller structures like galaxies. We consider two scenarios: one in which the
model only describes dark energy; and one in which it additionally entirely
substitutes dark matter. We find that the best model to explain data is the one
in which we have General Relativity and only stellar contribution. But while in
former scenario General Relativity is still statistically (Bayesian) favoured,
in the latter one the alternative model is as much successful and effective as
General Relativity in matching observations. Thus, we can conclude that even
objects like NGC1052-DF2 are not in contrast, and are not obstacles, to the
study and the definition of a reliable alternative to General Relativity.
