I'd recommend using SSIS as its purpose is for developing ETL processes. If you want to stay within I would use a pass through approach via open query vs a distributed query like you're using. Meaning, send your statement to be executed on the remote server and have it pull the results back. Make sure that the remote server has proper indexing for the statement it's running.
insert into dbo.claimdetail fields
where exists (select * from LinkedServer.prod1.dbo.ClaimsToPull
where CN = cdclno and
WN = cdwkno)
INSERT INTO claimdetail (col1,col2,...)
SELECT col1, col2, ....
FROM OPENQUERY (LinkedServer, 'SELECT col1, col2, ... FROM clmdet c WHERE EXISTS ( SELECT 1 FROM prod1.dbo.ClaimsToPull p WHERE c.Col = p.Col AND CN = CdClNo AND WN = CdWkNo')
Here is a great article from a MSDN blog: