Hi,
2 options
1) If I read your info correctly, the right thing to do would be to check what's happening in your HR system, as this situation shouldn't really occur. It's not so much a question of whether it's needed for expenses: the system sees data in IT0003 is inconsistent and it doesn't like that. Not sure how this inconsistency is created and dealt with in HR
2) As you don't need the time retro trigger in the travel system, you should be able to clear the field in ALE config. Then it won't bother you.
On a different note: I've never seen a convincing case, why travel & expense should be a system of its own. Why not have it in the HR or FI box? It's a residual of the old days, when security concepts weren't understood, so separate systems were used instead of proper authorisations.
Ever thought about consolidating?
It may not be worthwhile any more with SAP Travelmanagement on its death bed and a switch to Concur likely soon, but if you intend to run it for another 5 years or so, consolidating may still be a good move.