If you`re interested in researching your state`s policies on returned checks, check out the table below to better understand your rights in this regard. Deposit and fees for pets – An amount that is separate from the deposit held by the owner in case of damage due to the fact that a domesticated animal lives on the site. Some landlords may also add a monthly fee so that the tenant has the right to let a pet reside in the rental unit. Maybe. From an owner`s point of view, the answer depends on whether or not their right to terminate is stipulated in the rental agreement. For a tenant, it also depends on the written lease, but also on national law, which can leave room for the tenant to withdraw from the lease without damages or other costs. .