  In a recent FTC by Tremblay {\sl et al} (2009 {\sl J. Phys. A: Math. Theor.}
{\bf 42} 205206), it has been conjectured that for any integer value of $k$,
some novel exactly solvable and integrable quantum Hamiltonian $H_k$ on a plane
is superintegrable and that the additional integral of motion is a $2k$th-order
differential operator $Y_{2k}$. Here we demonstrate the conjecture for the
infinite family of Hamiltonians $H_k$ with odd $k \ge 3$, whose first member
corresponds to the three-body Calogero-Marchioro-Wolfes model after elimination
of the centre-of-mass motion. Our approach is based on the construction of some
$D_{2k}$-extended and invariant Hamiltonian $\chh_k$, which can be interpreted
as a modified boson oscillator Hamiltonian. The latter is then shown to possess
a $D_{2k}$-invariant integral of motion $\cyy_{2k}$, from which $Y_{2k}$ can be
obtained by projection in the $D_{2k}$ identity representation space.
