Duplicate Permissions

Some of my files have two "Everyone" permissions. One that is set to the norm and one that is set to "Custom". The "Custom" setting is preventing a program from moving and renaming files for me. I have tried changing the permissions of the folder that contains the files and then using "apply to enclosed items...". This hasn't worked, the extra "everyone" setting is still there. How can I get rid of (or change it to read and write) the extra permission without having to change each file individualy (+20,000 files)?