Your reel reels trips are the washable type.
I usually take the reel assembly out of the cabinet since it's relatively easy to pull the reel shelf out and then clean them while on the bench.
I use some luke warm water with a couple drops of dish soap added, about a quart should do it. Saturate a small terry wash cloth with the solution and ring it out. Gently wipe the reel strips down to remove the dust, avoid pressing too hard and creating a crease. Wipe dry with a terry cloth towel. Do not wipe the inside of the strips with the damp cloth. Use fine hair paint brush to break the dust loose then blow the dust out with some compressed air.
While you have the reel tray assembly out give each one of the reel position photo eyes a couple puffs of compressed air to clear any loose dust that's accumulated.