We tried our best but still could not find a new tenant. We will have lost rent more than one month .
It costs $200 to do carpet and house cleaning. It costs $250 to change a new range hood and two window blinds.
The insurance agent told me that it is not a legal reason. If the tenant sue us, will it be covered by liability insurance?
Why would you bother, the other Realtors gave you sound adivice, consult a Real Estate Attorney. Andrea has spelled it out for you quite well, if it were me I'd return the deposit , you have a new tenant why bother with it, move on.
The reality of the situation is if a tenant doesn't want to live there, you probably don't want them to stay as tenants. They will end up being resentful and probably be very difficult.
As a landlord myself, I would try to work with them so you can find another tenant. Since this is not your case you will need to see if you have any recourse.