It’s always a good idea to strain a finish before brushing or spraying it to remove dirt and other unwanted particles. It’s especially important to strain water-based finishes because small bits of finish often solidify in the can, and rust that forms around the lip of the can may fall into the finish.
Commercial strainers are widely available wherever paints and finishes are sold. These strainers are much easier to use than any homemade cloth system you may think up.
Straining always involves using a separate container, which can be the spray-gun cup itself if you’re spraying, or a jar or plastic container if you’re brushing. It’s best to brush from a separate container anyway, in order not to introduce dust and dirt your brush may pick up back into your main supply.