A human 'generation' is considered to be about 25 years, give or take 5 years depending on the century you are speaking of. So you would have to add about 20 or more 'greats' to the grandmother to push the date back to the 1400s.
There's no clapper in it, looks like it may have been used to drink from and hangs from a string or chain. Could it be a portable drinking cup? Just my first WAG of the day...
Gongs are basically flat or bowl shaped. Bells can have an internal clapper or be designed to be tapped with an external hammer.
Whatever size it is, it is a low-quality souvenir-type item. It is most likely made of brass, whereas decent bells are made of bronze. This item was made some time after 1940. The story about it being centuries old is hogwash.