  In this note we prove that if a closed monotone symplectic manifold admits a
Hamiltonian pseudo-rotation, which may be degenerate, then the quantum Steenrod
square of the cohomology class Poincar\'{e} dual to the point must be deformed.
This result gives restrictions on the existence of pseudo-rotations, implying a
form of uniruledness by pseudo-holomorphic spheres, and generalizes a recent
result of the author. The new component in the proof consists in an elementary
calculation with capped periodic orbits.
