Feedback Gain Loss of Transimpedance Amplifier
I suspect that you have a significant AC signal (or noise) superimposed on your dc signal that you are unaware of. The cap would usually get rid of these AC effects. Basically as the AC signal/noise gets bigger it clamps against the power rails and this is where you see what appear to be non-linearities.

Try looking at the output using an oscilloscope to confirm this.