The grease is from melted hamburger fat from a barbecue. The deck is
well aged lumber (exposed year round to New Jersey temperatures, rains
and snows, but shaded most of the time) that has never been painted or
sealed. So far, I've tried, separately, dish detergent, bleach,
something similar to 409, and ammonia with limited success. Next I'll
try, separately, laundry detergents (because of their enzymes), TSP,
oxalic acid, water-rinseable auto degreaser/carb cleaners, and an oxygen
bleach like sodium percarbonate.

Any othe suggestions? If the above or your suggestions don't work, I'll
use my belt sander. It doesn't matter if any of the treatments
temporarily alter the appearance, as natural weathering should restore
the grayness.

Thanks.

Ray