If I understand your layout, the rag is likely lying in a dry pipe between the new toilet opening and the other toilet and maybe a shower connection of some kind. I would first try a Shop-Vac to see if I could suck it out. Theoretically, if everything is vented properly, you shouldn't suck much yuck back. Be sure your shots are up to date just in case.
Caution: I am NOT a professional plumber.