There will most certainly be an agreement with the bank, for the â€œcash for keys programâ€ that you will be required to sign. If you have gotten that far, the answer to your question is in that agreement.
Typically, whether youâ€™re entering a program such as this or simply selling your home, items of this nature are considered fixtures in the property and are not â€œusuallyâ€ removed from the home.
Either way, you should speak to your bank representative; they may be able to help you out with that.
Also, you should contact a Realtor in your area; they will be able to advise you as well.