Total Commander

I use the synchronization function to update my backup with the latest files. This backup I also use for other computers to synchronize. And I can see with the synchronization the other way around which files are not present any more on the leading device. But I cannot delete older or obsolete files on my backup. The directory synchronization only shows them. Now I delete the files manually, an option (with care) in the synchronization would be useful.

Just filter/show all files that are "leftover" on one side, use Ctrl+A and use the context menu (RMB) with either:
<- Delete left
-> Delete right

And depending on the sync task at hand, TC also offers to optionally delete files in the "Synchronize" dialog box (like with the "asymmetric" sync option, which is intended for backups BTW).