Your neighbor may just have eclectic tastes, but the pie pans hanging from her tree probably serve a practical purpose. Aluminum pie pans work like armor, in a way, protecting the tree and surrounding plants from its deer and bird enemies. If you can stand their odd appearance, the pans make for one of the cheapest animal pest deterrents.
Birds can really do a number on trees. Woodpeckers can peck holes through them for food, to create a nest or just to show off. Many other types of birds eat fruit right off of fruit trees, or the blossoms right before they bloom, preventing any fruits from forming. Birds, however, scare easily and hesitate to return the site of fright. When you hang pie pans in a tree, light reflects off of them during the day, which visually frightens them. This will not work as well at night without supplemental light, but on a windy night, the sound will scare them as well. Also, birds are not as active at night.
Deer can damage trees by nibbling away at their leaves at all times of the year. Male deer can cause even more severe damage by rubbing their antlers against the branches or trunk of the tree right through the delicate inner layers. Pie pans scare deer in the same way they scare birds, by sight and sound. They usually work for only a short amount of time, however, until the deer become accustomed to them.
For the least amount of damage to your tree while trying to deter these animal pests, tie the pans with string to the branches. Hang them so that the pans sit close to where the deer and birds usually injure the tree. If you want to use the pans as a sound deterrent as well, string them close together so that they hit one another when moving in the breeze. Move the pans every three days so the animals don't get used to them in the same position.
The most effective means for keeping birds and deer away from your tree is to alternate your deterrents every so often. Substitute aluminum foil for the pie pans after a few days. Use targeted motion-activated sprinklers or cover the tree completely with a bird net or surround it with deer fencing. You can use noise repellents as well, but know that this will probably not only disturb your sleep, but the sleep of your neighbors. Chemical repellents targeted at birds and deer tend to work, but you may have to reapply after each rain.