The Wizard is really just a listing of backup history records in MSDB on that local server. This wizard is not necessary to do backups. In fact, you should run a process to purge backup history on a regular basis. When I do a SQL Server Health Check for a client, I consider it a finding (relatively minor but still a finding) when this history is purged.
I am wondering if you are attempting to restore to a different server which also has that database on it?
Instead, choose Device and browse to your backup file. You'll see the right backupset to restore to inside of that backup file.
The dialog here is sort of a helper if you are restoring on the same server where your SQL Agent backups are taken but if you take backups in different ways, if you clean up history or if you are restoring to a different server, that dialog is likely not so helpful.