DO NOT USE GREASE
Grease of any type is the wrong thing, and i keep hearing about copaslip which also is the wrong thing for bike brakes, but its become kind of an urban myth.
The proper stuff to lube the piston sides is silicon lube,and in particular 'Hunters'
Hunters silicon lube is the one hope use and highly recommend. Its really cheap and a small bottle will literally last decades.
https://www.biketart.com/products/hope-silicon-lube?variant=40809527214259
