You drop a linked server with sp_droplinkedserver. Obviously, if you have queries that refer to the server, these queries will stop working.

To find instances of these servers in stored procedures, you could do:

SELECT object_name(object_id)

FROM sys.sql_modules

WHERE definition LIKE '%SERVERNAME%'

Hopefully the server names are distinct enough to make this query useful.

Note that if it there are queries in client code, SSIS packages etc referring to these servers, the query above will not find them.