External emails sending to exchange distribution groups which include contacts with external email addresses tend to be blocked with “relay not permitted” because exchange sends the mail to the external contact with the original FROM:external@address.com to the external MX.

Get-DistributionGroup xxxx@xxx.xx | fl rep*
ReportToManagerEnabled : False
ReportToOriginatorEnabled : True

Switch both parameters:

Set-DistributionGroup xxxx@xxx.xx -ReportToManagerEnabled $true -ReportToOriginatorEnabled $false

source of solution:
https://social.technet.microsoft.com/Forums/en-US/cbd9bd18-533e-461e-93ef-113dc30ac7b4/external-mails-to-distribution-groups-not-sent-to-external-contacts-due-no-adressrewriting?forum=Exch2016MFSM

possible caveat: return-path empty, could not reproduce this problem on Exchange 2013