When does an improvement become part of the property?Tenants want to install disposal

[Amanda Thompson]

Our tenants want to install a new garbage disposal. They would be purchasing it, and they asked if they had permission to install it. I made sure to let them know we would not be maintaining it and they were responsible for it. My husband (we own the property and I manage it through my business) said he would professionally install it for free (to make sure it was done correctly) but once the appliance is installed, it becomes part of the property and the renters can't take it with them when they leave. I read through the lease carefully and it doesn't specify what to do in this situation (something to add to future leases). The property originally had a garbage disposal (which is now leaking) but the owner has phased out having garbage disposals in rentals and offered to come remove the disposal (at no cost to the renter, of course). 

Do you agree that this type of improvement becomes part of the property? Or do you think the renter should be able to take it with them when they eventually move out?