  In this note we prove that if a closed monotone symplectic manifold $M$ of
dimension $2n,$ satisfying a homological condition that holds in particular
when the minimal Chern number is $N>n,$ admits a Hamiltonian pseudo-rotation,
then the quantum Steenrod square of the point class must be deformed. This
gives restrictions on the existence of pseudo-rotations. Our methods rest on
previous work of the author, Zhao, and Wilkins, going back to the equivariant
pair-of-pants product-isomorphism of Seidel.
