Hose your pool filter down. That's it.
Yes, a garden hose with a regular nozzle on “jet” or “cone” is enough for ninety percent of cartridge filter cleanings. No chemicals, no pressure washer, no soaking.
The cartridge fibers are fragile. A pressure washer shreds them. A chemical soak degrades them. All you need is to blast the dirt out from between the pleats — work from the inside out, and spray at an angle so the debris pops loose.
If it’s greasy or stained after hosing, then a quick soak in a filter cleaner (TSP substitute or a commercial spray) might help, but that’s once or twice a season, not every time. And rinse thoroughly afterward.
You’re better off cleaning it more often (every two weeks during heavy use) than trying to deep-clean a caked-on filter with harsh methods. A $15 spray nozzle beats a $40 bottle of acid.
Don’t overthink this. Five minutes, done.