TSQL retrieve backup date from database after restore
Answer from author's comment converted to community wiki

select  top 1 
        s.backup_finish_date 
from    msdb.dbo.backupfile f 
left outer join 
        msdb.dbo.backupset s 
    on  s.backup_set_id = f.backup_set_id 
where   f.logical_name  = '&lt;name of mdf-file&gt;' 
order by 
        f.backup_set_id desc


In case the original MSDB is not available, or backup history has been purged, the data is available within backup headers. Use RESTORE HEADERONLY to retrieve the header contents. In the header, there's about 60 pieces of metadata; refer to the Microsoft documents for detailed description.

For example,

restore headeronly from disk = N'&lt;path-to-backup-file.bak&gt;';