Patrick,
A few things: those Fast Compression checks are there for your protection and are something native will not do for you. If a full backup, for example, were accidentally deleted from TSM, LiteSpeed would know, alert you, and optionally run another full backup to put you in a recoverable position.
But if you don't want / need those checks or if they are simply an Admin issue, you don't have to use Fast Compression. You can schedule regular full and diff backups to TSM as needed in LiteSpeed and backup without the extra validation. I will see if in a future release the TSM checks can be avoided in Fast Compression, but in the interim, LiteSpeed can back up to TSM without any extra checking.
I hope that helps.
Thanks.
--
David