What is the obstruction in this cleanout interior drainpipe?

http://www.savefile.com/files/2153090
(Click on the orange "Download File" button on the lower right.)

I have a drain that backs up after the water is run for about a
minute. I ran a snake as far down the pipe as it would go, but couldn't
find the clog. I got under the floor and found a cleanout access for
that pipe. I opened the cap, looked inside, and saw that there was
something that looked like an internal flap that I guess is supposed
to direct water towards the drain and away from the cleanout cap. I
poked at it, and it appears to be made out of some sort of foam-like
material, as it gave a little when I pushed against it.

But what goos is a cleanout access if you cant get into the pipe to clean it out???

Am I just supposed to tear that thing out of there, or what?