One solution would be to use replace() on document.body.innerHTML:

document.body.innerHTML = document.body.innerHTML.replace(/x/g, '*');

... wherever it is in a webpage, with vanilla JavaScript.

It doesn't matter where that character would appear...

... Wherever it will appear, it will be deleted.

The OP used wherever, It doesn't matter where and Wherever. He absolutely means everywhere. So,

document.body.innerHTML = document.body.innerHTML.replace(/x/g, '*');

does the job for him.

Yes, one solution, and also a good way to potentially destroy HTML element and attribute names present in the inner html and mangle attribute values, if the character to be replaced is part of an element name or attribute name or value.

Sure it addresses what has been asked in the question. And that includes the fact that it potentially destroys HTML tags or attributes.

Yes Zakk‭ your code worked for me (double checked) with:

document.querySelector('.new_pages').innerHTML = document.querySelector('.new_pages').innerHTML.replace(/\|/g, '');

Instead getting a | I got it deleted.

Thus, I think, your comment should be an answer which I'll gladly upvote and mark as worked.

You already wrote an answer. No need to (re)write mine. Glad my answer helped!