If you have booked a guesthouse, hanok stay, pension, hostel or private-style lodging in Korea and want to check what kind of registered business it is, start with Korea Tourism Organization's SafeStay service.
SafeStay provides an official permit-information lookup based on local-government licensing data. The current lookup covers foreign-tourist urban homestays, hanok experience businesses, tourist pensions, hostels and rural homestays. You can search by property name, region, address, permit date and operating status. Results show the lodging category and whether the record is operating normally, suspended, closed or otherwise inactive.
Do not treat a failed search as automatic proof that a property is illegal. SafeStay explicitly says some other accommodation categories are outside this lookup and should be checked with the relevant local government. Spelling differences, business-name changes and category differences can also make a search harder.
Practical next step: search the exact accommodation name and address before arrival. If the record is missing or the status does not match what you booked, compare the booking address, ask the property for its registered business name, and contact the relevant local authority or a Korea travel-information service before making a legal conclusion.