I rarely filter paper any more. I use the water method. I cook it out as cracklins and pour off the fat. You do not want to do this too hot. The closer to smoke point the fat gets, the stronger it will taste. I have had excellent luck putting trimmings in a (steel!) colander in the oven and avoiding the hot stove altogether. I put the colander in an enamel roasting pan. YMMV
For the water method you put solid fat and water in a pot and putting it all in the oven set at 200ish. Low temp, like doing ribs. I don't really want the water to boil, but that is ok.
I want the fat melted on top of the water.
Once the fat is all melted I turn off the oven and let it all cool together slowly. What happens is that the solids will precipitate. They will go to the bottom of the water or to the boundary between the fat and the water. Moving this to the refrigerator can accelerate the process. I like to leave it in the oven until I have visual that the solids have dropped.
After a fairly short period in the fridge you can pull it out. Pull the waxy solid fat off the water. You can break it if you need to. Any dark solids can be easily washed off with hot running water. Doing this three times will give you "triple rendered" fat.
I pour off all my sausage and bacon drippings into a jar which I keep in the freezer. When I get about a quart I water render it and then keep it in the freezer. This is lard, but remember it has salt in it from the curing. While my WV grandma used this for frying, I use it for pancakes, waffles, and biscuits.
Triple rendered venison fat will come out like soap. It will keep at room temperature indefinitely. I keep quart jars in the freezer when I have space. If I need freezer space. I just put them on the shelf in the basement. I give them to my soap-making friends.
I keep some for myself for cast boolit lube. I use 100% deer triple rendered deer tallow. Magic in hot revolver loads. I get 1300 fps plus with no leading in 44 mag. I have never cast for rifles, but I am interested to see how fast I can push these sometime. I've just always thought I should be paper patching at that point.