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.
But the calipers won't be new and zinc plated any more. Neither will the ends of the pistons where they bear against the back of the pad. Plus, for those that use those horrible stainless guides pressed into the iron caliper, for the pad ears, there is likely to be corrosion under then, making them a tighter fit. I agree that some folk really slather the stuff on excessively, but a tiny smear can, I think, be beneficial.
