The reason for this might be that those apostrophes are actually typographically nicer apostrophes. This can cause a small problem with the character encoding.
I have added some code to the latest developer version of TablePress, that should be able to handle this. Can you therefore please try again after installing the developer version from http://tablepress.org/download/tablepress-dev.zip ? Just replace the existing “tablepress” plugin folder on your server with the one from the ZIP archive.