How to add black mark in scanned pdf and scan it again quickly?

This is a scanned pdf file with black mark, and i think  the black mark is added by Adobe Acrobat because the black mark is too regular and without any noise dots.

The process may be: ( but i think this process is too complex )

1. scan the original paper file to scanned pdf file;
2. add black mark on scanned pdf file with Adobe Acrobat;
3. print step2 file and scanned again;

My question：

If you have a paper file and want to cover some words on it, how do you do?

I think these black mark added in the file, are not by pen and hands, because it is very square without any flaw.