Grease EZ Lube Bearings

I have a couple of questions when greasing the Dexter EZ Lube Bearings - I am using a standard size grease gun. I pull off the rubber cap - remove some of the old grease with a q-tip (my finger learned that the inside is sharp) and then pump in about 20 pumps of grease. I don't see that much grease come back out. The manual says to do this every 2,000 miles.

When cleaning out the old grease, how much do you have to remove? Is it OK if some grease remains in the cup and is held in by the rubber dust cap? I notice a small amount of grease on the wheel after travelling, but nothing alarming.

Anyone have any pointers for me - or am I doing this correctly? Thanks!