Show us a screenshot of your noise.
a) Are you getting a regular approximate 6 fine spikes along a slow 50hz or 60hz sweep?
b) Or, are you getting a continuous high frequency above 20KHz sine signal?
c) Or a low voltage squashed 50/60hz sine wave permeating everything?
If a), then your inverter may not be a pure sine wave type.
If b), then, some high frequency is leaking through the inverter's output DC-AC converter. This one you might be able to filter with a quality AC power-bar or a dedicated line filter.
If c), then your inverter is leaking current to your common ground, or you might call this a ground loop issue. Unfortunately, this might be by design and the only fix might be an AC line isolation transformer, at minimum for powering your scope.