SELECT localtab.field1 FROM LINKEDSERVER..REMOTEUSER.TABLE remtab, localtab 
WHERE ((remtab.rfield1 = 'value' OR remtab.rfield1 = 'value' ) OR (remtab.rfield2 = 'value' )) 
AND remtab.rfield3 = localtab.rfield3

SELECT * FROM OPENQUERY( [linked server],'SELECT 
  localtab.field1 
FROM REMOTEUSER.TABLE remtab
INNER JOIN localtab 
ON  remtab.rfield3 = localtab.rfield3
WHERE ((remtab.rfield1 = ''value'' OR remtab.rfield1 = ''value'' ) 
        OR 
       (remtab.rfield2 = ''value'' )
      ) ')

  --just the data that matches kind of    
;With MyCTE AS
(
SELECT 
  remtab.rfield1,
  remtab.rfield3
  FROM LINKEDSERVER..REMOTEUSER.TABLE
  WHERE remtab.rfield1 = 'Value'
UNION   
SELECT 
  remtab.rfield2, --the other column
  remtab.rfield3
  FROM LINKEDSERVER..REMOTEUSER.TABLE
  WHERE remtab.rfield2 = 'Value'
)

--now the join:
SELECT * FROM localtab
INNER JOIN MyCTE 
ON MyCTE.rfield3 = localtab.rfield3