The paper addresses this. To summarize

- The judges don't know the order of upcoming cases, but do pick when they're going to get food breaks. When they take these breaks shows considerable variation.

- Scheduling usually happens based on the ordering the attorneys arrive, and the attorneys don't express any conscious choice to try to game their arrival time.

- The paper also looks at what is likely to make a prisoner get paroled (e.g. type of crime, recidivism, etc.), and the cases that, without considering the effects of the breaks, are likely to result in parole do not seem to be clustered throughout the day.

The relevant passage:

A key aspect for interpreting the association between the ordinal
position of a case and parole decisions is whether an unobserved
factor determines case order in such a way that yields the
pattern of results we obtain. For instance, if prisoners without
a rehabilitation program or recidivists were somehow more likely
to appear before a food break, we would naturally find a greater
proportion of rejections occurring before the food break as well.
A number of procedural factors preclude this possibility.

First and most critically, the judge both determines when the
break will occur during the course of the day’s proceedings and is
unaware of the details of the upcoming cases. Thus, the judge
cannot decide when to take a break based on information related
to the nature of the upcoming cases. So, in the example above,
a judge cannot decide to take a break because he or she knows that
prisoners after the break will have no previous incarceration record.
Relatedly, the type of case (e.g., severity of the crime) that
the judge had just ruled on exerted no significant effect on the
likelihood of taking a break (Table S15). Furthermore, the large
variability in break start times and durations attests to the fact that
their occurrence would be nearly impossible to predict by any of
the prison staff involved in the parole proceedings.

Second, the ordinal position of cases is, with rare exception,
determined by the arrival time of the prisoner’s attorney. The
attorneys are sequestered in a room where they are unable to view
the proceedings of the board and, therefore, are unaware of any of
the rulings of the judge, how many prisoners preceded their client’s
case, or when and whether the food break occurred (after
the board’s deliberations, attorneys exit through a different door).
Thus, by design they cannot learn about the advantage of
appearing after a break. Indeed, a survey administered to a sample
of these attorneys after the primary data collection period
indicated that they were unaware of the effect of ordinal position
on rulings (see SI Materials and Methods, S2 for details). A similar
survey administered to parole board members (judges, criminologists,
and social workers) revealed the same results (see SI
Materials and Methods, S3 for details).

Because of the factors discussed above, we did not expect significant
correlations between ordinal position within either the day
or the session and the control variables in our data (SI Materials
and Methods, S4 and Table S16). Consistent with our expectations,
there does not appear to be a deliberate ordering based on the
characteristics of the prisoners (Fig. 3 A–D and SI Materials and
Methods, S4); certainly there appears to be no effect of a food
break on the type of prisoner appearing before the judge. Note that
although there was a slight but significant correlation between
recidivism and ordinal position in the day, this correlation was not
significant within a decision session, i.e., between breaks. Thus, it
cannot explain the spikes in favorable decisions after breaks.