situation in building a deck I will first rake the ground smooth after the posts have been cemented in, then lay down that Texaco Landscape Fabric that allows water to slowly drain through but weeds cannot come up. Then spread pea gravel over the area.
You can buy the fabric at any home center landscaping department. Fasten it down with cheap metal tent stakes or fashion stakes from coat hangers. This will work, but in your case you need to take this up as far up hill as possible under the deck so that water will not undermine the fabric and still erode under the fabric.
I do not know your decking spacing. But if the decking is screwed down you could consider tightening up the spacing to allow water to still ease through, but not at the rate it might be. Ideal spacing is about 1/4 inch. Spacing with green boards at this measure will become 3/4 or more after drying out of the lumber.