Stop earth from introducing noise to piezo circuit
Currently I am measuring the output of the piezos by connecting the
  output of the charge amplifier to a logic analyser


I believe it is extraneous earth currents causing this problem. You say that a logic analyser is connected to make readings and this presumably earths the "system" at one point. Then you connect another earth so now you have two seperate earths which a current can flow between. If the two earths are at slightly different potential then you get a flow of current AND if that flow is along a sensitive signal-return line you get interference pick up.

As an aside, if the logic analyser/lap-top setup is not galvanically earthed, it will tend to look "earthish" due to capacitance to ground - this can also cause higher frequency earth currents to flow as mentioned above.