It appears that team-based limitations and property-specific permissions are at odds with one another in your access settings. Changing team access to permit more extensive changes while preserving property-specific restrictions is one way to solve the problem. In order to prevent problems with team ownership, if your system permits it, think about using role-based access instead of team-based access. As an alternative, see if it’s possible to establish a new permission set that allows cross-team adjustments without granting complete access to every contact. Finding a solution could also be aided by looking at the support documentation and permission hierarchy in your CRM.