Need the model from the serial number tag as these came either both the Tuff Torq K46 and the General Transmissions RS800 [plastic housing] transaxles.
The K46 uses SAE15w50 motor oil and the RS800 use EP2 grease. Topping off K46 requires removing it.
If you has the RS800 the grease leakage can look a lot worst than it is. On those you replace the seals and drive the mower around for 30 minutes and then check the bottom of the unit to see it is heating up excessively. If doesn't then you are fine. Other adding grease is also a removal of the transaxle.
Here is how one can look and still don't need additional grease.
View attachment 66884
Adding oil to K46 is fairly simple but may need a new seal cap as they do age and go bad.
IF you have the GTI RS800 then I can try to post the instructions links on adding grease. But will require quite a bit of disassembly just to get to the add point. They are not very good. And really should let someone that familiar with unit do it.