Why do Nick's sisters want him to take back the engagement ring he gave to Alice in the novel, What Alice Forgot?

When Nick and Alice got engaged he gave her a ring that belonged to the family. In the present, Nick’s sisters are upset because they want the ring back. To them taking the ring back is their way of saying that Alice is no longer welcome amongst any of their family members, which is why most of the sisters refuse to even show up to an event if she’s there.