Powershell command permission to send to Distribution Groups

You probably have restriction on the DDG. Either AcceptOnly type, either RejectFrom type. To see these kind of restrictions you can user the attached expression. This will make an output with the following columns:
Name (of the restricted or allowed user or group)                         DistinguishedName (of the same)            mode (AcceptOnly or reject)                         DDGname (which has the restriction)

Each row has one user, so you can sort by this column, or do as you wish.

Get-DynamicDistributionGroup | %{$ddg= $_; 
$usrs = @($ddg.AcceptMessagesOnlyFromSendersOrMembers | select-object name, distinguishedname, @{n="mode";e={ "acceptonly"}}); 
$usrs += @($ddg.RejectMessagesFromSendersOrMembers | select-object name, distinguishedname,@{n="mode";e={"reject"}}); 
$usrs | select-object *, @{n="DDGname"; e={$ddg.name}}}

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the comment from @chris-dent should be the solution
when a new distribution group or dynamic distribution group is created in exchnage 2007 or 2010, by default the group only accepts messages from authenticated senders