  The starting point for this work is the family of functions
$\overline{p}_{-t}(n)$ which counts the number of $t$--colored overpartitions
of $n.$ In recent years, several infinite families of congruences satisfied by
$\overline{p}_{-t}(n)$ for specific values of $t\geq 1$ have been proven. In
particular, in his 2023 work, Saikia proved a number of congruence properties
modulo powers of 2 for $\overline{p}_{-t}(n)$ for $t=5,7,11,13$. He also
included the following conjecture in that paper: \newline \ %\newline \noindent
Conjecture: For all $n\geq 0$ and primes $t$, we have \begin{eqnarray*}
\overline{p}_{-t}(8n+1) &\equiv & 0 \pmod{2}, \\ \overline{p}_{-t}(8n+2)
&\equiv & 0 \pmod{4}, \\ \overline{p}_{-t}(8n+3) &\equiv & 0 \pmod{8}, \\
\overline{p}_{-t}(8n+4) &\equiv & 0 \pmod{2}, \\ \overline{p}_{-t}(8n+5)
&\equiv & 0 \pmod{8}, \\ \overline{p}_{-t}(8n+6) &\equiv & 0 \pmod{8}, \\
\overline{p}_{-t}(8n+7) &\equiv & 0 \pmod{32}. \end{eqnarray*} Using a truly
elementary approach, relying on classical generating function manipulations and
dissections, as well as proof by induction, we show that Saikia's conjecture
holds for {\bf all} odd integers $t$ (not necessarily prime).
