My iPhone 4, bought on 2010, stopped responding to home button clicks. The rear panel was just "a bonus".
Everything was ok. The guide from iFixit is perfect.
The Home Tech Toolkit has a Phillips #00 and a Philips #000 on it. None of them fits perfectly on the iPhone. But they do fit on the MacBook Pro. It is just weird. Luckily I have another screwdriver that did the job. None of the screws were harmed on the process.
Important: Print the screw template.