Frustrating permissions issue.

I recently moved my account to a new machine and have got an interesting permissions issue that's preventing me from editing a lot of files, even though my user has read/write permissions. If you look at the attached image, there is an extra "everyone" with "custom" permissions. I can't remove it although if I change it to read/write, I can edit the file but obviously I don't want to get everyone read/write access. How can I strip the extra stuff here? And i'd like to find a way to do it for my entire home folder since there are files like this everywhere..