What if she is no longer around?

Conduct a seance.

My thoughts exactly.

What court is going to make grandpa sign over the house to her based on a verbal contract with no witnesses?

In North America most verbal contracts (in this case, leases) have standing that defaults to the laws put in place. So if there's a law saying a landlord has the right to evict a tenant so long as they give 2 months notice, then the verbal agreement between the landlord and tenant must abide by that law. The point really is to make sure tenants and landlords are protected in cases like these. Grandfather rents to grandkid, then tries to kick them out claiming there was no written contract, well agreeing the rent-to-own was a verbal contract and therefore he cannot kick the kid out without notice.

A lease, sure. But that doesn't grant her ownership of the house.

Thats not how a contract works at all lol and definitely not held up in court

I completely agree. But the grandfather did op a favor sending the letter. Op now has in writing proof that there is an agreement in place. And no. One side can't void it on a whim. Try walking out on a regular lease and see what happens.