  In recent work, G. E. Andrews and G. Simay prove a surprising relation
involving parity palindromic compositions, and ask whether a combinatorial
proof can be found. We extend their results to a more general class of
compositions that are palindromic modulo $m$, that includes the parity
palindromic case when $m=2$. We then provide combinatorial proofs for the cases
$m=2$ and $m=3$.
