Actually, while PHP is useful, it is not necessary. I think you can telnet into mysql or something like that.
If you were to use a php script, here's some inefficient code:
Assuming your database was named "mydb" and your table was named "mytable" and included fields "id" and "text":
[PHP]
<?
$db = mysql_connect("localhost", "username", "password") or die(mysql_error()); //connect to mysql

mysql_select_db("mydb",$db); //select the database

$table = mysql_query("SELECT * FROM mytable", $db) or die(mysql_error()); //grab the table data

while($row = mysql_fetch_assoc($table)){ //do this for every row in the table

$newtext = str_replace(""", '"', $row['text']); //replace " with " in the text field and store that as the variable newtext

if ($newtext !== $row['text']){ //if newtext is different from the database value, then we need to update

$tmp = mysql_query("UPDATE mytable SET text = '$newtext' WHERE id = $row['id']", $db) or die(mysql_error()); //update the database

} //end if statement

} //end while loop

?>
[/PHP]
I only checked it for syntax but just IM me if you have any trouble.