Given the fact that the TYPO3 site is now working again, is clean and that the security hole has been identified and fixed, you can switch the website back online. However, there are some further things to do or to consider:
change (all) passwords and other access details
review situation: determine impact of the attack and degree of damage
possibly notify your hosting provider
possibly notify users (maybe clients), business partners, etc.
possibly take further legal steps (or ask for legal advice from professionals)
Depending on the nature of the hack, the consequences can be as minimal as a beautifully "decorated" home page or as extensive as stolen email addresses, passwords, names, addresses and credit card details of users. In most cases, you should definitely not trifle with your reputation and you should not conceal the fact that your site has been hacked.