The electrical signal of an electrode is not only caused by the concentration differences of ions, resulting from physiological processes. When two or more metals are immersed in an electrolyte, this will always result in a DC potential. The extra-cellular fluid is more or less equivalent to seawater, so can act as an electrolyte. The DC offset may also vary over time because the double layer of the electrode-skin interface can change a little, for example by sweat or movement of the electrode.
The DC potential is often not stable, but can vary within a large range. Actually, one can regard the offset potential as a battery. When Ag/AgCl electrodes are used, the variation of the offset will be limited (<100 mV). But when using for instance a stainless steel electrode in combination with a gold electrode, the offset can go up to several hundreds of milivolts (>500 mV). For this reason, one should always use just one type of electrode during a measurement and even then, the DC gain should be limited.
In the figure below, an example is given of a measurement where several types of electrodes were used. In the screenshot, the DC signals are shown, as well as the high pass filtered signals (in corresponding colors). The mentioned "cotton" electrode is a ceramic AgCl electrode that is wrapped in cotton. This electrode was especially developed to measure EEG using plain tap water.
TMSi amplifiers do not include any filters in hardware because signal analysis is better done afterwards in software (and is thereby much more precise than in hardware). Also, if one for instance wants to perform (either electrical or magnetic) stimulation, a hardware filter will cause huge filter artifacts (stimulation is measured by the electrodes, and the stimulus response will be a kind of impulse response for the filter). If one wants to remove the DC offset, a highpass filter at 0.5 Hz can be used in TMSi Polybench, Matlab, or any other application software.