Does the property company have the right to ask for the key after handing over the house?

No right. It is the developer's obligation to deliver the house to the owner. If the owner has paid the house price, the developer must deliver the house to the owner. Property management companies deliver houses to owners to fulfill their obligations on behalf of developers, only in the name of developers, not in their own names. The property management company refuses to give the owner the house key because of the owner's refusal to sign the owners' convention or other reasons, which is to attach its relevant rights in the property management contract to the developer's obligation to deliver the house, which is not in compliance with the law.