Hello I am a solicitor with 20 years experience. I will try to help you with this.
This is a contract situation and will be governed by the contract she signed with the Care home. I think it very likely that you would not have to clear the room immediately and might well have until the end of the period she has paid for to do it. The only way to know for sure is to discuss it with either your Aunt if you are able to or with the care home.