If by 'bottom cup' you mean carb float chamber, they are usually held in place by a nut. Some have anti backfire solenoid beneath, and that has to come off first, then float bowl can be removed via stop nut on its bottom.If you reversed the old filter, you have set yourself up to have the dirt trapped in it dumped into your carburetor next time you start it. Best to install new one, and to keep a spare. Always a good idea to replace it at in springtime when readying mower for cutting season.