I'd guess that it's pretty much factored into such observations.
And without lots of confirmatory observations, how can they infer that ALL distances to ALL galaxies, and hence the Hubble constant, is wrong?
The article says they're going to do more.
Moreover, M33 seems too close to use as an indicator of the Hubble constant; local motion can easily swamp it, as is the case for Andromeda, which is at a comparable distance.
My very fast (and thus worthless) research suggests that using eclipsing binaries, you get a solid reading on mass, thus an excellent clue as to what the absolute brightness should be. It gets a bit shaky from there, as your first question indicates. I don't see any indication that local motion affects anything. Maybe redshift, but that's not involved here. It's an independent method.
Or am I missing something here?
It's likely that I am. We need RadioAstronomer, but he's out of town.
Doing the Grand Master's bidding again, no doubt.....
By the way, they accounted for dust by observing at multiple wavelengths. Dust usually preferentially obscures redder wavelengths, so they can account for the dust by observing 7 or 8 filters and modelling for the dust from the expected spectrum (of an O9 star in this case).