Havent really LOOKED,but petcock should be removable and I guess the white piece your talking about is tank filter on petcock? This might be your best way. Just remove and clean while tank drains and can flush out? Will look when get to work!

 

the fuel petcock is just a plastic on/off valve in the tubing between the tank and the fuel pump and is just removed by taking off the fuel tubing.

the white part that im talking about is the hole in the bottom of the fuel tank that the fuel line attaches to and it is a box and has a fuel nipple that points toward the rear of the atv. it is soft plastic though, so i dont want to try to twist it off if it isnt even meant to be removed and break something.

 

Thanks for jarring my memory! have not had any fuel problems with hawkeye (JUST REAR DRIVESHAFTS) JMO is to back flush lines and petcock with air to avoid any possible damage. May be some other Hawkeye owners can chip in if have had same problem. Sorry couldn't be any better help! Good luck