Apostrophes replaced with slashes! HELP!

I need to take a site live tomorrow and I’m having some weird issue. Every time I type something with an apostrophe, a slash is added.

Example, when I type something like:

Pennekamp’s

…it ends up looking like:

Pennekamp\’s

This is primarily happening with the Ajax Event Calendar plugin, but I’ve been told it’s a WordPress issue and not a plugin issue. Does anyone know how I can fix this asap?!