Your data looks like a long term recording, but I cannot identify the time axis' scaling (is it seconds?).
In this case, the recording is rather meaningless in terms of distortion caused by common mode currents, I believe it's just the normal fluctuations caused by whatever the load / generator does. A transformer wouldn't change this behaviour. If nothing gets unusually warm (cables, filter capacitors, inductors), I'd consider the setup OK.
If you suspect too high common mode currents, you'd have to measure the actual currents in the earth / neutral / DC bus using a current clamp and suitable equipment (True RMS DMM, scope). Also measuring the inverters AC side with a good and safe differential probe might be interesting, but not necessarily useful for you. For measuring the common mode battery current, you'd have to put both conductors (Bat + and Bat -) through the clamp, so only the common mode current remains to be seen, assuming the battery doesn't have any more connections to the inverter.