I don't think you can easily hide that (or at all). What I have usually done is that I use List as display type and prevent user from selecting more than one option.
Names Default To Here(1);
dt = open("$SAMPLE_DATA/Big Class.jmp");
dist = dt << Distribution(
Continuous Distribution(Column(:height), Process Capability(0)),
Local Data Filter(
Add Filter(columns(:age), Display(:age, N Items(6), "List Display"))
)
);
filterob = (Report(dist) << Top Parent)[OutlineBox("Local Data Filter")];
filterob[ListBoxBox(1)] << Set Max Selected(1);
This might not be same for other versions than JMP19 as JMP19 did mess with the data filter display box structure.
-Jarmo