The FCC seems to have abandoned any concern about "consumer" equipment making line hash. Energy star mania has had some unpleasant side effects, by an R-lamp LED type by a major manufacturer. As handy as it is for servicing, I turn it off when testing!
A 4 ft LED shop-light from Costco is noise-free in comparison. I recommend them for benches more than 4-ft LED replacement T8/T12 tubes, that use line voltage to the bi-pins/tombstones and do create some noise as I just found out.
After you identify noise source, a portable AM radio is a good tool to determine if the inverter is conducting noise out via the line connection OR generating noise radiated mostly in proximity. This can be confirmed by moving the radio close by the refrig. and controls, then along its cord, then next to other AC circuits, wires, etc.
If noise drops as you move away then, like some electronic-ballast fluorescent lamps, is direct radiated but still may affect an AC-powered radio elsewhere in the house. I assume its compressor is well-grounded and shielded as any appliance would be.
An M-derived filter, using neutral/line to ground Y2-rated .05mf caps on both sides of a common-mode inductor, in line with the refrigerator compressor may reduce line-carried noise. Closer to the source the better, without voiding the short warranty.
I have had some success putting the cord receptacle-mounted filters from PC power supplies into 30s-40s consoles, especially if noise comes on the AC line from uncontrollable sources. Nobody seems to mind a grounded cord anyway. I have been able to tune AM easily on some sets, even in the basement. Other sets seem to have noise only on parts of the band with "peak" concentrations at certain frequencies. I have worse 60 hz buzz-type noise during the day, I have shut down every branch breaker in the house and outbuildings yet it persists. One radio with an oversized filter cap momentarily plays clearly when you pull the plug out, nailing it as line-borne noise.
Using a Euro-model Sanyo 9v AM portable and surveying on bad days, wondering if its from coming from the only other neighbor on the pole transformer, 300 feet away. The noise seems to vary considerably but is coming from the line. Switching phase at the breakers sometimes helps but as a light or something else is switched on, the noise returns. House wiring, though grounded, seems to make a nice repeater system.
I'm just happy having 3 AM stations that play music. But from 20 and 60 miles away, so just during daylight hours.