I learned that a long time ago when I was a student and wanted to submit a pdf generated by a trial version of some software as an assignment and was trying to be clever and cover the watermark that said unregistered with a white box.

When opening the file in my slow computer, I could see all the rendering of the watermark happening in slow motion until the white box would pop up on top of the text.

It's actually quite easy to open the pdf and see that there are several different elements per page to the document, eg the main text, an image, the footer, the title.

Randomly removing these by trial and error will usually quite easily allow you to find the watermark and nix it, with the advantage that even a sophisticated recipient will not be able to find out from the pdf file what the watermark was.