Just did ours the other day. I've done it both ways noted above. This time I had a MerC "Water Separating Fuel Filter" (the one that looks like a spin-on oil filter) full of gasoline. I put that in the small baking pan I use under the oil filter and added another few ounces of gas. Just enough to cover the "fins" with the arrestor on edge. I rolled the arrestor in the gas like a little Ferris Wheel and brushed the in- and out-sides with a toothbrush. Quickest, cleanest job I've had on it. Maybe 10 minutes work. Spray Carb Cleaner does really well, too, as they've noted. That and "Brake Parts Cleaner" which works really well removing oil.
OIL - Don't oil the standard Arrestor. Noted above but I'll repeat that to be sure you don't miss it. Arrestor design keeps a backfire flame front from escaping its confines. BUT it's possible for the oil in the plates of a dirty Arrestor to catch fire.
Arrestor design takes "ignition" out of the Ignition-Fuel-Oxygen "Fire Triangle" and cleaning it takes "Fuel" out. We don't want to put "Fuel" back by adding oil.