Well, not frame by frame, but yes, in AE.
This is actually a video tutorial I want to do, part of a series of removing things from footage, since that is a large part of vfx work.
The easy explanation is:
1 - track the post-it note
2 - take a frame of the footage into Photoshop and paint the post it note out.
3 - bring the clean frame back into AE, apply the tracking data to it, then roto it so it only covers the little post-it.
4 - add grain and blur to match, if necessary.
Of course, it sounds easy written out like that, but you'll come across many problems trying to track tons of things throughout an entire shot, then you will most likely have some work to do with rotation and scale on the patches, and you'll be rotoing lots of things back over top of the patches, etc, etc, etc...
But, that's essentially how to do it.