For the most part, I think the answer is, unfortunately, that your neighbors will have to be understanding for a while. Three year olds scream a lot, and that's just a fact of life. They are frustrated when the world doesn't work the way they think it should, and they don't know what to do about it, so they scream.
As far as dealing with the tantrums, read the related question/answers, and I think you'll find that neither of our answers strictly says you should let her just scream. Rather, the idea is you should help her calm down, while understanding that sometimes the screaming will happen and it won't just instantly go away.
You can sometimes help that calming down process, either by having a soothing item (a blanket, stuffed animal, etc.), or by helping her manage her physical symptoms - with my children, for example, asking them to take deep breaths helps both by managing the physical symptoms and sort of as a mantra to help calm the mind. Again it's not instant, but it does help them get to a place they can process things better (and did when they were three).
But I'd caution you against even considering the neighbors here. If you do, you're going to add additional stress into your parenting relationship. When the goal becomes "shut up the child" rather than "help the child process her complex emotions", you both fail to help your child grow, and you end up stressed out and likely will react in inappropriate ways.
Apologize to your neighbors, but do so in a polite manner that makes it clear that you aren't changing things for them.
I'm very sorry that our children's noise bothers you, but unfortunately this is part of child development and I'm afraid there's no way for us to simply stop her from screaming. We're working with her to help her understand and process her emotions in a more positive way, but as with any child this will take a fair amount of time.
