There is a pressed in check valve that has a brass disc in it. Most kits don't include it and care must be taken in installing a new one. Here is a name of a guy that is very good on Zenith Carbs.
Larry Isgro Carburetors Inc
1604 Argyle Road
Wantagh, NY 11793-3144
(516) 783-1041
If you want it done right, I would give him a call. I have been fooling with Zeniths for over 50 years. I don't even want stinky carburetor cleaner around any more. But If I had a Zenith that needed repair, I would Larry do it.