I got a kick out of your answer Joe2. lol His idea may deflect a few sound waves but probably not enough to make a difference. A lot of money for a bandaid. I'd try a heavy set of window curtains first. Hang up a bunch of towels first before buying any expensive curtains though to see if it helps.
The new heat pumps are quieter than the older ones but moving it may be the best solution. However, I would not recommend that anyone intentionally damage a high priced heat pump unit and end up in prison by removing the caps on the schraeder valves on the lines and then illegally release freon into the atmosphere. Hopefully you get along with your neighbor. It is not uncommon for HVAC techs to forget to tighten the valve caps after removing their pressure guages or the vibration of the unit itself causing the caps to loosen or the o-ring under the valve cap can fail also but then the valve needs to leak also which some do which is why they put caps on them. Don't let the air out of your neighbor's tires either.
You might check with the zoning department to see if a heat pump is allowed in a 5' sideyard setback. That is part of the house which may be a zoning violation. If it is too loud, you may have a lawsuit against your neighbor over that. Besides common law issues, most places have noise ordinances and some limit stereos, etc. to 50 decibels at a certain distance. Also many zoning ordinances limit fences to 6' high without a variance.