Change the words that are already in a PDF, rather than adding new text on top. Open the document, click into a line and edit it. This is the tool for correcting a typo, updating a date or changing a name in a document you no longer have the source file for. How cleanly it works depends heavily on how the PDF was produced.
A scan is a picture of a page and contains no text to edit. Run OCR PDF first to add a text layer, though be aware that editing recognised text does not change the underlying image.
PDF stores positioned text runs, not paragraphs, so replacing a short word with a longer one has nowhere to reflow to. Keep replacements close to the original length where you can.
That happens when the PDF embeds only a subset of the font - just the characters actually used. Typing a character that was not in the original subset forces a substitute font.
Each page has to be analysed before it can be edited, so pages are processed as you reach them rather than all at once up front.
Files are uploaded over an encrypted connection and processed on CoonTool's own server, not in your browser. The working copy is deleted automatically once the job is done, and in any case within 24 hours. Nothing is stored permanently and no account is required.