Yep! Insects can use their legs, mouthparts, as well as other specialized structures for grooming. In addition, some beetles actually use water to wash off dirt and contaminants. Other insects make and secret substances for cleaning. A common example of this is ants using formic acid as a disinfectant. Then, similar to monkeys, bugs like bees and ants conduct social grooming. This helps with the colonies overall health.
I've rescued wasps from the pool as well even though they & I are mortal enemies. 1) it was in the water with me & I didn't want it considering me a liferaft, and 2) smushing it was not an option. It flew away, hopefully to tell its brothers that I'm worthy of a brief ceasefire.
Most bugs do groom themselves, but here's a fun fact! Bed bugs don't groom themselves, and this makes most standard insecticides ineffective, because they won't ingest any of the poison they might get on their bodies!
Another fun fact: bed bugs are the fucking devil and I don't hate them, I haaaaaaaaaaaaaate them.
Being clean is a matter of life and death! They have hygiene issues we don't see at our scale. They deal with tiny things like mites we don't even think about.
Couple examples: Extra crap is extra weight and causes balance issues. Tiny blob stuck to a wing? You're flight systems are hosed. Something tiny stuck to a single lens on your compound eyeball is going to throw your visual system. Even predators are prey, gotta be at peak performance. Probably 1,000 things I'm not thinking of ATM.
Imagine your skeleton is on the outside, plate mail if you will, your flesh fused directly to the underside. Now let me roll you in sand and see how well you function. Ouch. I pretty much destroyed a drone landing it on a river beach. Sand ate the gears, and that thing wasn't moving nearly as fast as insect wings.
Boric acid is wildly effective against roaches (and other bugs) precisely because they're such clean animals. They track through it and ingest the acid while washing up, burns their little guts out. Diatomaceous earth is so fine it gets in the chinks and physically grinds 'em up.
Watch any given insect for a bit, house flies are a great example. Constantly cleaning! The exceptions being predators like spiders and such. They have to remain chill to ambush prey.
tl;dr: Insect anatomy is fine tuned to a level us biguns can hardly grasp. Dirty is not an option.