Hi ,Guido, Linda A,
For your comment about a closed distribution list, I understand Did you mean that Membership approval is closed, so all other members' requests to join are denied? If yes, you could turn on Membership approval as the following command :
Set-DistributionGroup -Identity "Dog Lovers" -MemberJoinRestriction 'ApprovalRequired' -BypassSecurityGroupManagerCheck
Or
Set-DistributionGroup -ManagedBy