Updating one DB field from a remote DB

I get no error when I run this but the field Res_Org does not gst updated in the table CSEA from the value on the remote DB.

ALTER PROCEDURE [dbo].[ADD_CSEA_Org]
      -- Add the parameters for the stored procedure here
AS
BEGIN
      -- SET NOCOUNT ON added to prevent extra result sets from
      -- interfering with SELECT statements.
      SET NOCOUNT ON

UPDATE tblTo
SET tblTo.RESP_ORG = tblFrom.RESP_ORG
FROM Tbl_CSEA tblTo

INNER JOIN [Linked Server].ICSS.dbo.ICSSLOGS tblFrom
   ON tblTo.LOG_ID = tblFrom.LOG_ID


END