Bhagavad Gita, Chapter 2, Verse 26

But even if you were to take this to have constant birth and death, even so, O mighty-armed, you ought not to mourn for this.

Even if you believed the soul dies and returns, that still wouldn't be a reason to grieve.

Krishna doesn't need Arjuna to agree on how the soul works. Even under a completely different view of death and rebirth, the logic against grieving still holds up.