Removing the reflection completely from the entire clip would be very difficult. You may be able to roto the first bit where it's most apparent. You'd want to make a clean plate of just glass with the first man's jacket color under it, then paint that over the original clip. Wish I could be of more help, but there's no easy way of doing this.
You could try a few tricks with channel operations and blending modes, but generally there's no perfect and easy way to remove such stuff, even more so since everything is pretty much already quite drab colors with little contrast.
I would trim the shot to just the footage necessary to tell the story first because this is going to be tough. The worst parts are where the guy in the dark blue suit provides a background for the reflection just as the door closes.
Here's how I would approach the fix. Photoshop's healing brush is probably the best tool for generating a clean plate I would try painting a frame at a time in Photoshop being as careful as you can to remove just enough to break up the reflection instead of completely remove it. The dirty window is your friend here. Here is a side by side comparison I did of a screen grab in Photoshop that took only 5 strokes with the healing brush. The closing door should hide the flicker completely if you don't get too aggressive and you remember what you were painting.
Retouch just enough frames to cover the worst of it.
Check playback to make sure that you are not introducing flicker that is worse than the original problem.
When the door closes and the reflection is pretty much hidden stop. Back in AE take a close look at the shot and in the few remaining places that movement by the camera operator give him away ADD some grunge to the shot that can be faded in and out slowly to hide it just to cover the telltale movement.
You've got to remember that the audience isn't going to be scrutinizing every frame and that hiding only the give away parts and throwing in a little extra grunge is the best way to handle this problem.