A dispensing closure system, a package including the same, a method of making the package on a form-fill-seal machine and a method of dispensing flowable products from the package are disclosed. The package includes an openable port in a wall in communication with the package's interior. The closure system comprises a fitment having a hollow body member, a resilient valve, and retainer assembly. The body member is secured to the package's wall and encircles the openable port. The valve is held in the body member by the retainer assembly, which comprises a retaining ring and a cap integrally connected to each other by a frangible connection. The cap includes a handle which may be pulled to break the frangible connection to remove the cap and thereby expose the valve for a dispensing probe to be extended therethrough to dispense the product.