Mondial Front Wheel Bearings

Yup, that's correct in what you are saying! Make sure it is good clean or flush it (with terpentine). Blow it dry with an air compressor and let it dry out for at least a day.

Put the mouth of the grease tube between the bearing balls and grease it. This way you will press the grease to the back. If no tube you will need to do it with your vingers.

 

I didn't remove the nut on mine. I simply soaked and cleaned it up, then packed it full of grease. One of those grease needles for your grease gun will come in handy to get at nooks and crannys. It is not like a typical car with an inner and outer bearing, there is only the one you can see. IIRC, the bearing housing is basically sealed from the back anyway, so you probably wouldn't gain much. I've got a couple of thousand miles on mine since doing it with no problems. Believe me, whatever you jam in there will be a big improvement over the glop you took out.
By the way, while you are in there, are you redoing the ball joints? The lowers on mine were kind of scary worn out once I had them apart. Keep up the good work!