If you can see this check that
A packet which arrives on eth0 and leaves on eth1 will pass through
which filter table chain?
I made this name up.
The packet probably does go through MANGLE at some point, but there is a better more obvious table in one of the other answers.
Input devices routed to output device goes through the FORWARD chain.
Only packets destined for the localhost go through INPUT.
Only packets created by the localhost go through OUTPUT.