xcaer, like barkingdog, I too have some very strong thoughts on the matter. You are taking risks and I have to be really honest, if you were my neighbor and this has happened more than once on any level, I probably wouldn't be too happy. I am VERY happy to hear that your dog inflicted no physical damage to the other dog. But the owner and her dog were 'traumatized' to some degree without a doubt.
Imagine if another dog threatened or attacked your dog in your yard. Imagine if they wounded your dog. Try to imagine if it was a terrible wound, or worse. You would be furious, so would I and depending on the relationship you have with your neighbour...they may still be very upset. The reason doesn't matter because there is NEVER a good to be attacked on your own property. There is NO DEVICE that I know of that will keep your neighbour's safe from your dog 100% of the time. Anti bark collars do NOT work 100% of the time. The threat that happened to your neighbour's dog is likely still in your neighbour's mind. Your neighbour probably doesn't feel safe anymore, I know I wouldn't.
I don't know how big your property is, but If I were your neighbor I'd want your yard 100% fenced or your dogs on leash 100% of the time. Simple as that.
If after my dog was threatened/attacked, if I saw that these things were not done, I'd be very very upset and as much as I love all animals I'd probably call animal control. It is legally your responsibility to protect other people and property from harm from your dog. It's also part of being a good neighbor.
Please please try to rectify this situation to your NEIGHBOUR's satisfaction. The risk level to your neighbour's dog should be zero.
Although it's true that your neighbor could also put up a fence, and possibly split the costs - your dog was the attacker, and your dog may well attack again.
After your neighbors are protected, then group obedience training for your dogs is highly recommended. And I'd neuter the intact dog as well.
Hope that wasn't too harsh - just calling it like I hear it and trying to help you avoid potential future conflicts with neighbours and potentially police officers/animal control.