We discuss transport through an interferometer formed by the helical edge states of a quantum spin Hall insulator. Focusing on the effects induced by a strong magnetic impurity placed in one of the arms of an interferometer, we consider the experimentally relevant case of relatively high temperature as compared to the level spacing. We obtain the conductance and spin polarization in a closed form for an arbitrary tunneling amplitude of the contacts and arbitrary strength of the magnetic impurity. We demonstrate the existence of quantum effects which do not show up in previously studied cases of weak magnetic disorder. We find optimal conditions for spin filtering and demonstrate that the spin polarization of outgoing electrons can reach 100%.