Seller renting the house for a week

[Fred Ramos]

We just recently purchased another investment property but this one came with a little twist. usually when we've purchased, the unit has been empty and we have been able to screen the tenants and decide who to rent to. in this case, the seller wanted to rent the house back for a week while they move out.
Our concern is this, though we have been paid for the 7 days and in the contract it allows for a longer stay at so much per day, what would be our recourse should the seller decide to stay longer and not pay or not take care of the property?
usually we would have SSN's, employers and such but this time we have no such thing.
do we just make a rookie mistake? How can we rectify? We feel out of control.