Mortgage Broker or Lender, Florida
As a renter you have rights but not sure how this would apply to a fixture in the back yard. The buyers or the seller agent may be recomending that this 'termite ridden' feature be removed to help sell the house - not exactly bad advice. I would suggest working with them instead of digging your heals in the sand - they will be the ones deciding if you get your deposit back, if you can stay 1 extra day if needed due to some last minute issue ( moving trucks break down, storms delay moves, etc).
The weekend is coming up. I would suggest asking for a few days to move the boxes into the garage, spare bedroom, wherever.