Given an algebraic automorphic representation of a genus two symplectic group over a totally real number field with an Iwahori-spherical component at a finite place $w$, we shall show - following Sorensen - that there is a congruent automorphic representation with a tamely ramified principal series component at $w$. Thus after a base change to a finite solvable totally real extension, the level at $w$ can be lowered.