That sock thing is Honda's idea of a fuel filter. It will come off, there's a plastic ring at the open end that slips off the petcock itself.
You can't just drop the assembled petcock in nasty chemicals, though. There's a rubber disc in the valve in some types that would be damaged, another type uses a cone shaped metal valve but it has rubber O-ring seals.
If yours has screws holding the front plate on it can be completely disassembled and cleaned easily, you should use some silicon grease on reassembly to lube the valve action - on the rubber disc or the metal cone and O-rings. Dielectric grease works fine.
The riveted ones are serviceable if you drill out the rivets and then tap for a 6-32 screw to reassemble it.
Internal parts are not available for the riveted ones, and I doubt if they are for the screw-together ones. If it is just clogged, you can usually clean and lube it and you're OK. If it's leaking out around the lever then sometimes flipping the rubber disc solves that, or replace the O-ring on the other type. You should be able to find a standard O-ring that fits.
