Generally the only way back from any form of hacking or unintentional changes is to rely on your backups!
Sorry, not true in all cases. Backups especially recent ones (last 4 months or so) are likely to contain the exploit. Relying on the backups will only put the exploit back. Again and again.
While 1.5 is ok, you should think about moving to 2.5 at some point. In the meantime here is what you need to do.
It is suggested to do all of the following. Failure to follow the suggestions below may leave your site vulnerable to being hacked again in the future.You must state what version of Joomla you were using when when the site became hacked. This can make a difference as to how we approach your individual situation.[ ] Run the
Forum Post Assistant / FPA Instructions
available here and are also included in the download package.
[ ] Ensure you have the
latest version of Joomla.
Delete all files in your Joomla installation, saving a copy of the configuration.php file. Replace the deleted files with fresh copies of a current full version of Joomla (minus the installation directory), and fresh copies of extensions and templates used. Upload the copy of your configuration file.
Only by replacing all files in the installation (including extensions and templates) can you be sure to remove the backdoors inserted and hidden in files and directories More detail can be found in the security Checklist 7 link below.
[ ] Review
Vulnerable Extensions List[ ] Review and action
Security Checklist 7 to make sure you've gone through all of the steps.
[ ] Scan all machines with FTP, Joomla super admin, and Joomla admin access for malware, virus, trojans, spyware, etc.
[ ] Change all passwords and if possible user names for the website host control panel and your Joomla site.
[ ] Use proper permissions on files and directories. They should
never be 777, ideal is 644 and 755 and 444 for the configuration.php file.
[ ] Check your htaccess for for any odd code (i.e. code which is not in the standard htaccess supplied as part of the Joomla installation).
[ ] Check the crontab or Task Scheduler for unexpected jobs/tasks.
[ ] Ensure you do not have anonymous ftp enabled
Note: The forum post tool will work with 1.0.x, J1.6.x, J1.7.x, 2.5.x versions of Joomla. 
