Acrobat's electronic signature is saved as a file on your computer. If you open a pdf on your computer, you can extend the permission to modify the document by verifying the signature. If someone else's computer doesn't have this signature file, it can't pass the verification, and there will be corresponding protection strategies.
The landlord doesn't have to worry about others rebuilding the signature file with the information you signed. Each signature file contains different encryption properties. You can't create the same signature file unless you copy it to others yourself.