Backplate for satin nickel deadlock
If you want it to match the color of the satin nickel hardware as good as possible, I would recommend cutting it from... Satin Nickel.  The same companies that make door locks also make "kick plates" for the bottom of the door, and smaller "push plates" that are made to push open a door that doesn't have a knob (normally seen in commercial doors).  Here is an example of a push plate.  You could use one of these like a piece of sheet metal to cut whatever size and shape you wanted.

They also sell door reenforcement plates that are used to cover up damage:



Example here

Most home stores will have these in stock - I randomly picked Home Depot to link to, but these are common items if you know what to look for.