Fuel line cleaning help

[72jenny]

I bought a 72 C10 lwb that had been sitting for a few years with gas in the tank. As a result the fuel was all gunked up and nasty. I went ahead and took the gas tank out and cleaned it pretty well. However, now that I am ready to start my truck I am noticing that I have gunk in the fuel filter next to the carb still. I think it might be in the lines and possibly a little leftover debris from cleaning the tank.

How you I go about cleaning this? Since I thought I had cleaned the tank I filled it with new gas so I really don't want to have to drain it all. My fuel filter doesn't seem to block most of the gunk so would buying a second fuel filter possibly help as a temporary solution until the little gunk leftover is fully ran through the system?