New pads are not "old parts" so you can only be refering to the carriers, which if worn, need to be replaced. Grease is not a replacement for metal.
Grease only attracts crap.
We had one of those, it was a fixture on one of the ramps. There was a magnetic pick-up that was put on the suspension, and I seem to remember that it had a strobe light and an electric motor that you pushed onto the tyre to spin the wheel up.
Like the manufacturers, I use no grease anywhere when I fit new pads. The only place I lubricate, like the manufacturers, is the slide pins.
Where does it say to put grease on the back of pads or pad ears?
I usually clean the caliper up with a wire brush and these. There should be no need to remove the carrier.
What type of grease are you thining of, and where do you intend on putting it?
The word vagina comes from the latin word for sheath. And "sheath" is what we used to call a condom.
A vagina and a sheath are both places to hide the sausage.