Record not getting filtered using like clause
Your search pattern contains a wildcard character [,
you should enclose it in brackets or use ESCAPE character like this:

declare @SearchRecord table (searchkeyword1 varchar(100));
insert into @SearchRecord values
('"Affiliate" means'),
('"Agent''''s Rate of Exchange" means'),
('["Aggregate Total Commitments" means'),
('["Agreed Security Principles" means');

select * 
from @SearchRecord 
where searchkeyword1  like  '![%' ESCAPE '!';

select * 
from @SearchRecord 
where searchkeyword1  like  '[[]%';


All this is described here:
LIKE (Transact-SQL)