it´s a german lastname, if was in Czech Rep., former Bohemia so was in any case of later sonamed Sudeten Germans. why do you note the czech theme? do your Jungreithmayr have connections there?
and yes phonebook shows most in state Upper-Austria. and looks to be also a VERY usual name .
for Austria quite a few in relative to the size of the country.
name word by word
Jung = young
Reith, think about reit(en)= ride
Mayer would be also an own lastname, comes about = tenant of a farming
no idea what really meaning ALL in one word or came about. often some parts of a name can have an old dialect meaning, so not always clear or just not in same expression in present days like in old times.