The term you are likely looking for is "attractive nuissance". and part of ownership involves keeping one's things on one's own property.
Not only are they increasing the local predator load, but they are putting your flock at risk of disease, when the corpses of the neighbor's birds are brought to your property.
An anonymous call to animal control might be in order - any chance you got pictures of the dead bird on your property? Evidence of that sort can help.
To be clear, while the birds are on their property, they are "free ranging" - none of your business. When the birds crosses the property line, it is "at large". Whole different set of rules applies.