I have an Arlo Essential wireless doorbell that I want to install on a steel security door.
As shown in the photographs, the mounting plate holes can almost perfectly match with one hole in the door plate.
Is it safe to drive a screw through the mesh?
Screwing through the mesh of a steel security door could damage its integrity and security. It is crucial to make sure that any alterations do not weaken the door or introduce potential vulnerabilities.
Widen the holes slightly, then determine the bolt/washer/nut required for that sized hole. This will be secure, however if you want to reduce the torque/pressure against the door/doorbell, a thin metal plate between the door and washer/nuts provides a more secure solution with less strain.
It may be excessive, but it also keeps the doorbell from being affected or tampered with on a side that is often flush with an inaccessible surface (wall/door).