Fragrance Sachet Paper Stuck to Wood Cabinet?

I placed a fragrance sachet inside my linen closet only to find that within a few days it was stuck to the side of the cabinet. To remove it, I tried pulling the paper sachet off the wood surface which destroyed the sachet, but left the paper stuck to the wood. I have tried label removers, soap and water and have not been able to remove the paper and residue. Any ideas on solving this problem?