Peel and Stick wallpaper does not damage walls when you install the peel and stick wallpaper properly.
As long as you follow the instructions and install the peel and stick wallpaper correctly then there should be no damage done to walls when you remove the peel and stick wallpaper.
I have removed peel and stick wallpaper before from a house because I didn't like the wallpaper and it did no damage to the walls underneath the wallpaper.
If the peel and stick wallpaper leaves any residue on the walls surface the leftover residue can easily be cleaned off the wall with soap and water or gentle adhesive cleaner.
Peel and stick wallpaper is an easy to install wallpaper and does no damage to walls when used properly.
However if you're renting a home you should consult with the landlord first about it.