I took the air cleaner off my to-35 and soaked it in kerosene for over night.
the next day as others said I back flushed it until the fresh kerosene came out looking clean.
lot of dirt in mine after all these years.
then I let it air drip/dry for another 24 hrs as I did not want to pull a bunch of kerosene into my carb.
fired the old tractor up and she ran great.
no problems, tractor is a 1957 model and to knowledge all maint the air filter has ever gotten is changing the oil and cleaning the pan of oil at the bottom of the air cleaner.
I would not take that mesh wire out of the filter, have read horror stories about the fact you cannot get it back in there and not available to buy new, but your call on that one. they must have used some type press to insert the wire mesh screen.