When players trying to interact in claimed chunks where they are not permitted to do anything (not allies), show a warning in the action bar that tells them they are not permitted to [action].

For example, if a player tries to destroy a block, instead of just silently cancelling their action, show a red message in the action bar ‘You cannot build in this area.’ and when they're trying to open chests ‘You cannot interact in this area.’

This way players will be able to learn about the claimed feature faster. One of the newest players on our server accidentally thought they have bugged and couldn't build anything, so they tried to rejoin a couple of times and then gave up until later we told them that there is a feature preventing them from building because of the claim.

Also, note about using action bar (in the same place where you show team name), so you don't spam the chat :)