Extracting data from SQL Server linked server
Check the link server setup and see HOW the users connect to the link server. This can be done by going to Server Objects in SSMS -> Linked Servers -> [Link server name] ->  right click then select Properties -> security tab. It can be done without a security context, using the current login's security context, or it can be done using a specific login. Find out which account is being used and then make sure that account has access to the table on the linked server.