  We consider a large family of dynamical Belyi maps of arbitrary degree and
study the arithmetic monodromy groups attached to the iterates of such maps.
Building on the results of Bouw-Ejder-Karemaker on the geometric monodromy
groups of these maps, we show that the quotient of the arithmetic monodromy
group by the geometric monodromy group has order either $1$ or $2$. Prior to
this article, a result of this kind was only known for quadratic maps (Pink)
and a few examples in degree $3$.
