“let your peace come upon it.” This is an idiom. If a person was worthy, the guest would bless the house, and that blessing would involve “shalom,” translated “peace” but really meaning “total well-being.” If the apostles were well received and well treated, they were to bless the house with shalom. Jesus instructed his disciples to let their shalom fall on those who graciously took care of them.
“let your peace return to you.” This is an important lesson, because most of the people Christians witness to do not believe, and often Christians become self-condemned about this, thinking that they must have done something wrong or are not a good enough witness. But Christ taught us that when people reject the Word of God, the witnesses are to let the peace they have been offering to others return to them.