Using sed steam editor to replace a specific string of regular and special characters

It seems that you also want to strip away the semicolon, too: Hence:

sed -e "s/'/'/g" file > file.new

or without output redirection, modifying in-place:

sed -ie "s/'/'/g" file

The 'g' modifier signals that a global substitution (i.e. all occurrences in each line) is desired.

If you have a string to filter this will look like:

echo "hello'world"|sed -e "s/'/'/g"
hello'world