In my view, this falls under fair use.

If you have a private copy of a printed newspaper, you're free to tear out a page, draw pen-mustaches, wrap a fish in it, make a paper airplane, solve the crossword puzzle incorrectly, wipe yourself, basically anything you like - for your own amusement.

I don't see how your private copy of the webpage bytes should be any different.

In both cases there are very clear boundaries: you can't redistribute derivative works without permission & attribution (copyright), you can't publicly broadcast, etc. Everything else should be fair game.