Quip Enterprise customers can control external sharing using External Sharing Restrictions. You can restrict all external sharing, then optionally add individual trusted partners as authorized recipients.
Additionally, we have a number of security features that we can turn on for Quip Business and Quip Enterprise customers. One of those features enables you to restrict public links to your domain and warns people when they are sharing outside their team. If you'd like to enable those features for your team, just email us.