$t$ is a square $\pmod{2^n}$ if and only if $t\equiv 1 \pmod 8$

Question

Show that $t$ is a square $\pmod {2^n} \iff t\equiv 1\pmod{8}$, given that $t$ is odd and $n \ge 3$.

I've tried proving forwards using Hensel's lemma, but got stuck.