What database? Basically you would remove that from the search and create a column based on that result.... something like:
REPLACE(ColumnName,'''','')
Would give you the column without quotes.. so you could create a query or view with that in your SQL statment like:
SELECT *, REPLACE(ColumnName,'''','') AS ColumnWithoutQuotes FROM TableName
Then you can use that query for your serch which would include that new column without quotes you could search on.