If you have a database backup, you can use the 'Recover data from an unattached content database' functionality to recover only a single list and then re-import that data into SharePoint.
To do this, you'll have to restore the database, either to another instance of SQL that you can then access via SharePoint (recommended), or to the same instance but as a different database name/file name. Note that you need to be careful during this step if using the same instance that you don't overwrite the database that is currently in use. Taking a backup of the current production database before you start is important. If possible use another SQL instance, or even a test/development instance if you can as there is then no way you can impact the production farm.
Once the database backup is restored to SQL and the appropriate accounts have been added (if required) to allow SharePoint to access the content database, the following steps can be used to recover information:
- Navigate to 'Backup and Restore' in Central Admin
- Select 'Recover data from an unattached content database'
- Ensure that the database server to be used is correct, and modify if required.
- Enter the database name, and optionally authentication information if required.
- Select the operation to perform, initially browse content.
- Drill down through the site/lists and libraries until you have found the one that you're interested in and then select 'export site or list' from the available options. This generates a SharePoint backup file containing the list information.
- Restore the list backup using the PowerShell Import-SPWeb command (yes, seems strange, I know, but that's the command to use against the file produced), preferably to a new location so that you can then decide which information to copy back into the list that you were working with.