If you don't have renter's insurance, then the wall needs to be repaired in a manner that leaves them in the same or better shape than when you moved it. What that costs depends on what needs to be done. The entire panel may need to be replaced. If this is the case, the entire wall, and possibly the room, will probably need to be repainted so it matches. If the wall is textured, has wainscoting, or has wallpaper, the cost goes up.
In theory, it could be $100 or several thousand.
And you do need to let the landlord know. You don't want to deal with a lawsuit if she finds it after you move out.
Your sister was doing more than just "leaning" on that wall. Houses from the 1870's have VERY thick and sturdy walls When doing demolition for updating and remodeling, one needs to take a sledgehammer to those walls. That being said, repairs could be pricey, since those walls are woodlath and thick plaster.
1st of all do NOT try to hide it from the landlord. You cannot have anyone do any work on the property without landlord knowledge & permission so you cannot hide it from them. You need to tell the landlord, let them fix it & pay what ever it costs. A small patch should not be real expensive especially if they have their own staff do it.
20 bucks...maybe a little more...a hole that big what you do is square it up....maybe a rectangle...need to expose one inch of the stud ( 2 by 4 )..find a scrap piece of sheetrock and nail it in place...spackle the seam, let it dry and paint it..
My sister was simply leaning on the wall and her elbow suddenly punctured the wall and made a hole that's 8 by 8 inches approx. The part of the wall it was had not been restored since the original house was built in 1870s. How much will I have to pay to have it fixed? I preferably don't want the landlord to know.