Is.. you did not mention what brand of reel you have. If it is an ABU/Garcia or Quantum, they do not recommend using grease (or oil) on their drag washers. Just replace them and make sure all the surface areas they contact are free of grease or anything else. The drag washers are less than a dollar. Use CRC Electrical Contact Cleaner to remove old grease and oil. You can get it at NAPA stores.

If you have a Shimano reel, they do use grease (not oil) on their drag washers. It is called amazingly enough, Shimano Drag Grease. It is about $5.00 for a small tub which will last a long time. Once again, drag washers are cheap.

I would buy new washers, available at most reel repair shops. If you have a Shimano, rub Shimano Drag Grease into the washer before installing it. If you have one of the other reels just install them dry. Clean all the drag surface areas with CRC, not matters which brand you have.