Like Don said, the more of the old grease or oil you get out the better, it will just dilute the new grease. Fill it with mineral spirits to clean and thin whats there, then suck it out or drain it if it has a plug. You could crack the side cover open a bit and drain it that way.
I used a heavy plastic bag full of grease with one corner cut off, think of a pastry chef, and squeezed it in.
Joe