Well, sorry your neighbors haven't been direct with you. However...........
part of being a responsible animal owner is keeping your animals on your property. It's really not responsible to just let your animals roam. Your solution needs to be confinement to your property, not just out of their garden. Chickens are strong creatures of habit, and since they've been accustomed to eating and bathing at the neighbors, you might need a strong fence to change that habit. A 4 foot fence can be temporarily added to with rolls of plastic mesh, some folks use stakes to add height and string wire at intervals making rails on the top. You can look into clipping wings. You can use electric poultry netting to re-train them to your property and/or allow them to range in your yard. Some folks have used water spraying but you have to be very, very dedicated to change the habit.