Only residue I know of is water. I can see it encapsulating organic debris from the ocean floor though, if you want to consider sediment to be a residue.
Production methods to date, including Japan’s, involved releasing the methane from the hydrate latices while still in place. Only the methane is brought to the surface.
Japan used a depressurizing method to release the methane in place. Reference: http://www.rigzone.com/news/oil_gas/a/124983/Japanese_Firm_JOGMEC_in_Ice_Gas_Breakthrough