Unfortunately that wouldn't work as this is information inside the PDF itself so it has nothing to do with the file hash (although that is one way to track.)

Now that this is known, It's not enough to remove metadata from the PDF itself. Each image inside a PDF, for example, can contain metadata. I say this because they're apparently starting a game of whack-a-mole because this won't stop here.

There are multiple ways of removing ALL metadata from a PDF, here are most of them.

It will be slow-ish and probably make the file larger, but if you're sharing a PDF that only you are supposed to have access to, it's worth it. MAT or exiftool should work.

Edit: as spoken about in another comment thread here, there is also pdf/image steganography as a technique they can use.