Ok, you got me there. Those are not the same filters as my 002 nor your 003 or the other ASK 002 you had. Is that an acorn nut?
Or is that the first filter can, the one closest to the control panel? If so, that is the strainer. Since the two pumps already have strainers, this is actually to remove emulsified water since the shaking during operation tends to suspend water droplets...
anyhow, getting long winded here, if that is the first can, you should be able to run on fresh diesel as the filters will also block water. This just prevents overloading of the filter elements with water.