Why doesn't an FFT pitch filter fully 'mute' the selected pitch range?
First of all, tell us more about the filter. Is it really a brickwall filter, or are you actually using a low roll-off or low cut-off filter? In the latter case, it is perfectly normal, when using a high cut-off filter, the low frequencies decrease with -6dB per octave below the specified frequency, and are not completely gone. Roll-off is the same, but with less dBs per octave. (either 4,5 or 3, can't really remember.)

If you did use a brickwall filter, there is another possible explaination: 

A phenomenon in psycho-accoustics is the hearing of a low note where it is not there, but when the harmonics (= overtones) are there. Every base tone has different overtones. (Really, if multiple overtones are there, there is really not much ambiguity.) The human brain actually processes these overtones and adds the base tone.