> Moving forward, if I do have sensitive data to hide, I'll place a pure-color mask over the area, instead of a blur or pixelation effect.
Alternately - don't pixelate on a stationary grid when the window moves.
If you want it to look nicer than a color box but without giving away all the extra info when data moves between pixels, pixelate it once and overlay with a static screenshot of that.
For bonus points, you could automate scrambling the pixelation with fake-but-real-looking pixelation. Would be nice if video editing tools had that built in for censoring, knowing that pixelation doesn't work but people will keep thinking it does.