Hello, So there are a couple things to point out here. First your device, the DAQPad-6016, doesn't have a -1 to 1 volt range, so it is using the -5 to 5 for you. Also, from the specs, the absolute accuracy at that range is 2.003mV. The test panel shows about -0.3mV to 0.5mV at its peaks. So that appears to be well within spec. In the picture I attached, I was using an M Series device (better accuracy than the DAQPads) with an available range setting of -1 to 1V, so the difference between your pic and mine is understandable.
Looking back at the specs for the DAQPad-6016, it says the absolute accuracy at +-10V range is 8.984mV. So a 20mV noise is certainly not acceptable, but it isn't 20x the spec.
Is there a chance that you were injecting some noise on your signal that you were measuring (in your initial post)? Could you look at the signal with a DMM or something else to see if it is the source (or connecting wires) that is injecting the noise, and not the DAQPad?
-Alan A.