Pump filter - necessary or not?

Our pond is about 100galls. Black plastic liner, 40 percent coverage
with plants, rocks in the bottom etc

In it are 13 fish. A mirror carp, a ghost carp, three red goldfish,
five orange and black goldfish and three golden tench.

The pond is crystal clear and the fish are very heatlhy. (they all do
push ups and play five a side football each evening). In the pond is
a pump which pumps water up to a filter and, from there, back through
a copper pipe which empties into an old 'stone' shell shaped object
which collects the water and allows it to drain out via several holes
back into the pond from a heaight of eighteen inches or so.

The problem is that the pump blocks up every couple of days and
drastically reduces the water flow. At the pump inlet is a small
piece of plastic foam (presume this is quite normal) and this block of
foam gets jammed with green slime and gunge.

Can I remove this block of foam at the pump inlet and rely on the
filter box doing the job by itself. This box contains a lots of
pieces of plastic tube cut into 40mm lengths and on top of these are
two further pieces of foam, one blue in colour and knobbly, the other
is black and, well, smooth really.

If I can do this and ensure a continuous flow of water, we can go away
for more than two days at a time. The wife really could use the
holiday, so please help!!

Patrick