The oil is just separated from the grease from age. With the top open, just soak up the oil with paper towels and replace the grease with new. Use a spoon or something to scoop out some grease and wipe it in to the gears. That is all you need to do. Don't go to crazy. Put about the same amount in that is there now, plus a bit. That's really all there is to it.
You don't want to over grease it. Use the same amount that you see now. Some has melted and separated but what you see is about what it needs