The simple answer is to not put microphones too close to the dampers. Move the mics towards the tail of the instrument a few inches and angle them down towards the strings. You also may just have an instrument with a loud damper set (which makes life really unpleasant when you need to record it).
Entire books could be written on piano micing techniques... When I need to close mic, I usually go high-end, low-end a few inches out from the hammers. In film/acoustic situations, I'll put the mics out near the curve of the instrument. For classical solo recording, I use a stereo pair 6 feet out or so from the instrument.
Each has their own distinct sound that will or will not work depending on the kind of recording you are trying to make...
--Ben