I conflated your question with "do satellite galaxies show the influence of dark matter in general...ie. Do they HAVE dark matter?", but I think I answered your question at the bottom regarding orbits and velocity dispersion as you mention.
Tidal dwarf galaxies (TDGs) are typically observed to lack dark matter. TDGs are different from “regular” dwarf galaxies which are typically dark matter-dominated and likely of primordial origin and are thought to have formed in their own dark matter halo and have distinct evolutionary histories from a TDG.
TDGs form through galaxy collisions/interactions and they do not accrete dark matter through this process. The dark matter in the halo from the parent galaxy is too dynamically hot to be accreted and only baryons are accreted. This result does fit in with the dark matter paradigm (not specific to MOND but doesn't necessarily exclude it), as these galaxies are NOT primordial in origin. What DOES challenge Lambda-CDM (cold dark matter) and may support MOND is as follows:
So we know Lambda-CDM predicts isotropic distributions and random kinematics for satellite systems, but we don’t observe this. Instead, we find that dwarf satellite galaxies exist on a disk or plane that likely co-rotates with the main galaxy. We see this occur in the Milky Way, Andromeda, and Centaurus A. TDGs fit into this puzzle because phase-space coherence may make better sense if the satellite galaxies were initially TDGs. In the work by Muller et al. 2018, 14 of the 16 satellites with kinematic data follow a coherent velocity pattern aligned with the long axis of their spatial distribution.
With the data we have on satellite galaxies and their massive host galaxies, it’s getting more difficult to state that we just can’t see the dwarf satellite galaxies (known as the missing satellite problem which LCDM doesn't explain). It seems the simulations that predict a halo-like distribution of satellite galaxies have some serious flaws. Perhaps there is something not being accounted for or the idea of dark matter is incorrect. In any case, being able to predict the distributions of satellites remains a problem.
Most astronomers still "vote" for LCDM because dark matter is "needed" to explain the large structure we see today and the gravitational mass density exceeds the baryon density. The problem is we still don't know what dark matter is and are running out of options. I am personally agnostic until we have more data.
MOND predicts that the velocity dispersion will vary from the Newtonian regime when the external field of the host exceeds the internal field of the dwarf satellite (external field dominant quasi-newtonian regime). To confidently discriminate between Newtonian dynamics and MOND in the velocity dispersions of satellite galaxies requires extraordinarily high accuracy, which is unlikely at the current time. See http://astroweb.case.edu/ssm/mond/EFE.html for more details and equations.