The source is at a distance $x \pm \Delta x$ (assuming the sources are coincident). The lag between the gravitational wave signal being detected and the gamma ray signal being detected was $t \pm \Delta t$.
The difference in signal speeds is
$$\Delta v = c -\frac{x}{t_0 + t},$$
where $t_0 = x/c$. Dividing through by $c$
$$r = 1 -\frac{\Delta v}{c} = \frac{x}{x +ct},$$
and the assumption has been made that the two signals were emitted at the same time.
Then, if I have my error propagation formulae correct, the error in this ratio (call it $\Delta r$) is
$$\Delta r = \frac{c \sqrt{x^2(\Delta t)^2 + t^2 (\Delta x)^2}}{(x+ ct)^2}.$$
If we assume $ct \ll x$, then this simplifies to
$$\Delta r = \frac{\sqrt{(\Delta t)^2 + t^2(\Delta x/x)^2}}{t_0},$$
where $t_0$ is of course very much larger than either $\Delta t$ or $t \Delta x/x$. This is why $\Delta r$ is of order $10^{-15}$, though I'm sure the authors did a more complex calculation of the uncertainty.
If the distance to the source were known via the Hubble redshift-distance relation (which is not the case here), then the uncertainty in the Hubble parameter would enter as a contributor to $\Delta x$, where $\Delta x \simeq x\Delta H_0/H_0$.
I think if you are comparing the speed of light to the speed of gravity waves, you are assuming that space has the same "refractive index" for both. Strictly speaking you are measuring the ratio of the speeds, not the ratio of the speed of GWs to the speed of light. i.e. Where I have used $c$ in the formulae above, you can use $v_{{\rm EM}}$ where that is the speed that the electromagnetic waves propagate. If the "refractive indices" differ, then of course $r \neq 1$.
Now looking at the paper itself (section 4.1), we see that the authors approximate $\Delta r \simeq v_{\rm EM} \Delta t/x$ (in my notation). This would appear to neglect any uncertainty in $x$, but if one reads on, we see that what they have done is use a minimum distance to define the maximum possible $|\Delta r|$ and assuming that the signals were emitted at the same time, so that the observed 1.74s observed delay is because the gamma rays travel slower. This minimum distance is the distance derived from the GW signal itself of $40^{+8}_{-14}$ Mpc, which is independent of cosmological parameters (see https://physics.stackexchange.com/questions/235579/how-were-the-solar-masses-and-distance-of-the-gw150914-merger-event-calculated-f).
The lower limit is obtained by assuming that there was some lag between when the EM signal was emitted and when the GWs were generated. This was assumed to be 10 s for the purpose of the lower limit quoted in the paper. The reason for this value is discussed at some length in the paper. Since 10 s is much larger than the observed lag of $1.74 \pm 0.05$ s, then the uncertainty in the distance is less importantant (i.e. it becomes an error in the error). They seem to have used the 26 Mpc minimum distance again, in order to arrive at the lower limit of $-3 \times 10^{-15}$ for a total lag of 8.26 s.
