Slow performance when using a synonym that is configured to use a linked server
Fact is both are same.

CREATE SYNONYM [Testsyn]
FOR [RemoteServer].[DBName].[dbo]
GO

SELECT *
FROM [Testsyn].EmpTable
GO

SELECT *
FROM [RemoteServer].[DBName].[dbo].EmpTable
GO


Optimizer just decode synonym to actual object,there after both will have identical query plan."[Testsyn]" will be converted to "[RemoteServer].[DBName].[dbo]"

Poor performance for synonym could be :

i) Because permission issue to synonym on remote server.You should check with DBA of both team.