i think it would be like this, right?
DECLARE @TermToTweak VARCHAR(30) = 'lowell@fake.com'
DECLARE @cmd VARCHAR(MAX) = 'EXECUTE AT(LinkedServer,''update P
set P.Email1 = ''' + @TermToTweak + '''
from MyDatabase.dbo.Profiles P
JOIN MyDatabase.dbo.Complaints C on C.ID = P.ID
where P.Email1 not like ''' + @TermToTweak + '''
AND C.DateBlocked IS NULL'') AT LinkedServer'
EXECUTE(@cmd)
Lowell