Sorry if I was a little confusing. When I've had to grease my own clutch I always hit the inside and outside. I made the mistake once of accidentally getting a glob of grease on the inside where the pedal connects and the first time the car got nice and toasty inside, the glob fell to my floorboard. I just didn't want anyone else to go through the fun job of cleaning grease from carpeted floormats
Usually when it's the throw-out bearing you won't notice the sound with the engine off since the bearing is not being spun. Since you said there's a new clutch, I'm assuming that the pressure plate was changed as well? Those can squeak a little sometimes when they're worn.