Q: After suspicion of a virus I erased the content of the drive and installed OS X Again. How can I restore a back-up from my time capsule without contaminating the drive again? Isn't the back up contaminated?

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At the time of this writing there are no virus for the mac in the wild that have been reported by any reputable securities lab, but having an email hacked requires no special or undermining software, only circumventing the security of the account from a computer, any computer anywhere in the world connected to the internet.

of you restored your entire drive and there was a corruption it's possible the corruption will still exist. If you have the data a more secure update from a "peace of mind" standpoint would be

backup, remove the backup drive

format the internal drive

reinstall the OS from the original disks or Internet Recovery if your mac supports it (yours does)

About OS X Recovery - Apple Support

reinstall any 3rd party software from the developers website or the original media

restore documents, photos, music and saved data from your backup, but exclude the applications from the backup for now.

this does not suggest your computer is contaminated, it's simply one method to contain contamination if there was one in the event you restore the drive.

[edit] no single method is ever fail-safe or fool proof.

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You never had a virus. There has yet to be one that affects the Mac OS directly. The closest thing to that was Flashback, which did behave exactly like a virus (infection occurs with no user interaction). All you had to do was visit a compromised web site. But it wasn't an OS X virus, it was a Java virus that used one of the numerous flaws in Java as an end-around to get on the system. If you didn't have Java installed, it didn't work. It was also patched against years ago and is deader than a doornail.

Can't say for certain Google doesn't do this, but I could find no reference that Google puts out such email notices.

If there ever was anything on your Mac, then yes, it will be duplicated on the TM backup as far back as whatever it was got on the system. If you know there's a clean point that can still be restored, restore it from that date. All other personal data will have to be retrieved from TM manually. That I can't help with since I don't use TM for my backups.

I didn't specify what kind of virus I thought I had, but if I understand it correctly it was just a Java virus?

It would be impossible since the only Java virus ever known to affect OS X is long gone dead. I was just mentioning it as the only virus to ever have been able to attack OS X. Though it did it through Java. There's nothing to find or remove.

"Virus" is a term often misused to mean any "bad software". The correct generic term is malware. Which is short for malicious software. This term means any software written to intentionally damage your system, steal passwords, etc. So malware refers to any:

Virus: Any app that can replicate itself via direct access.

Worm: Smarter than a virus. It doesn't need to be able to see a connected drive or use other direct sight methods to infect another device. Worms can actively find other devices across a network on their own.

Trojan: Dumb apps which rely on the user to get on the system. YOU have to install it in some manner.

Trojans account for almost 100% of active Mac malware.

Google does most certainly sends an email…

Didn't say they don't. I just couldn't (quickly) find a reference that they did.