The simile compares the ugly words to a group of buzzards.
Buzzards are a scavenger bird, preying on things that are dead or near dead. They are not considered good or kind animals. The buzzards sitting in a tree are just waiting to swoop down and devour the meal. The words are similar in that they get into his thoughts and mind, picking at whatever is left. It reminds the reader that Mr. Shiftlet is a damaged soul. He is not who the women think he is.
This is a reference to Biblical scripture. God said that HIs people (Christians) were as a city upon a hill. This means that we are an example of Christ before the whole world.