Gravity cannot transfer angular momentum between spherically symmetric bodies. However, the attractive force of the Earth and Moon, because it acts most strongly on the directly adjacent parts (and least strongly on the backsides of each) deforms these slightly elastic bodies -- and in addition causes tidal flows of the liquids in the Earth's oceans. The resulting "bulge" is not symmetric about the Earth-Moon line, but rather is advanced further around the Earth's spin axis by the Earth's rotation. The Moon then sees a gravitational field which has an extra lump on the side of the Earth spinning away from it. The additional attraction of this lump, the result of the tidal bulge shifted by rotation, exerts a torque on the Earth's rotation, slowing it, and a torque on the Earth-Moon system, shifting the Moon to a further orbit.
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