Go Easy ...

Just Put The 2 Single Quotes within the String if you want a single quote there.

update rem_reports set RPT_COLUMNS='Project Name, Division, District, Program, Purpose, Tract Number,Owner''s Name, Acreage, Acquired Cost, Estate Code, Remarks,
Method of Accomplishment'
where rpt_name='1019' ;

This will solve your Problem..

Thanks..