I would change fuel filter easy disconnect, if that doesn't fix the issue, your almost better off upgrading you fuel pump. I bought my aviator 310lph pump for 50 bucks on eBay with the fuel pump filter that snaps in at the bottom which is what you are referring to I believe. It's not hard undo straps that hold gas tank, pull out pipe to gas filler, disconnect the wire harness to fuel pump unbolt 8 bolts pull assembly out of tank, unbolt assembly and pull out your fuel pump with the filter snapped in at bottom of pump.
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2004 Mustang GT 5 Speed
Full Bolt Ons
12.1 @ 117.9 (1.7) in 1/4th
7.6 @ 92.1 (1.6) in 1/8th