I've already used a razor blade to cut around this window to where I want the wallpaper to be. So, to remove that paper that didn't come off I take a wet washrag--not dripping but good and wet--and wipe it along the paper so that I get the paper throughly wet. Let it sit for a minute to soak up the water.
Then I just take my fingernail and scrape off the paper. You may have to re-wet the paper several times to get it all to come loose.
After you're done getting that excess wallpaper off, then go back over that area with the wet washrag to finish removing any bits of paper and remove the glue that's there.
Now, the kitchen window was a bit more tricky, because that paper was stuck on that wall good! So, I've cut where I want to remove the excess wallpaper with my razor blade.
Then I just wet the paper good with the wet washrag, let it sit for a minute to loosen. Then I again just use my fingernail to scrape off the paper. Once the pattern portion of the paper is off, I just continue to wet and scrape, until it's all gone.
Compliments of LPCullen