Neighbor demanding me to stop using heatpump

In my house that is ~1,000sqft we have baseboard heaters and heat pump. We used to use heaters but our electricity bill was ~$400/mo which is too much for us to pay. We started using heatpump a bit more during the day (off at night), but our neighbor demands us to stop using it because they don’t like the “humming sound” that the fan makes. They already reported it to the city, but haven’t heard from the officials yet. The heat pump has a permit and inspection done, so I’m not sure what to do now.

On one hand, I completely understand the concern about fan, but it can barely be heard and we don’t want to be freezing at home.

Edit: I should add that one day they woke us up at 11:45PM literally BANGING on our door at least few times.