Y'know Krash, I thought about that. You very well may be right. Ted, verify that the small 'filter' isn't a check valve, designed to keep fuel from draining out of the pump.
This is a common problem as pumps get old. There isn't a rebuild kit for the check valve and it certainly isn't cost effective to change a good-working pump just because the check valve went south.
I added a check valve to my '59, just before fuel enters the pump. That way a good head of fuel keeps pressure on the valve to keep it closed, so the pump doesn't lose it's prime.
Tom, if you take the small 'filter' out and you're able to blow in either direction, it's a filter. If flow only goes one way, it's a check valve. - Dave