Stairglides are attached to the floor. After you have the stair lift removed, you shouldn’t see any damage to your stairs or carpet. The screws keeping the support brackets steady will leave a few small holes in the stair treads. Carpeting should keep them out of sight.
If you have wooden stairs, the brackets will leave small holes behind, which you can plug with wood filler. The holes should not pose a risk for damage, or make your stairs unsafe in any way.