  The element $P_2^1$ of the mod 2 Steenrod algebra has the property
$(P_2^1)^2=0$. This property allows one to view $P_2^1$ as a differential on
$H_*(X, \mathbb{F}_2)$ for any spectrum $X$. Homology with respect to this
differential, $\mathcal{M}(X, P_2^1)$, is called the $P_2^1$ Margolis homology
of $X$. In this paper we give a complete calculation of the $P_2^1$ Margolis
homology of the 2-local spectrum of topological modular forms $tmf$ and
identify its $\mathbb{F}_2$ basis via an iterated algorithm. We apply the same
techniques to calculate $P_2^1$ Margolis homology for any smash power of $tmf$.
