Permalinks, 404 errors, and non-wp related folder in wp directory

Okay, so my wordpress installation is located at https://www.example.com and is working flawlessly(with super cache plugin).

Now, I want to include a gallery using a 3rd party script at https://www.example.com/gallery/. I have it up and running and it is working properly if I go to https://www.example.com/gallery/.
But if I open an image in the gallery, the url goes to https://www.example.com/gallery/category-name/wallpaper-name/. This gives a 404 error on my wordpress theme.

The script has a .htaccess in its root folder(www.example.com/gallery/).

I am guessing that wordpress is interfering with my gallery.

How could I fix this problem? Thanks!