Well,
First fact is that on whole word there are millions of callers with restricted caller ID.
You are lucky because from your point of you it is only one calling party.
With this fact we can do:
Write one rule in custom app like
Exten => s,1,if ${callerid(num)}="" goto... Check on VoIP-info what are operands for expression.
Or you can use asterisk db to store allowed callerid.
In asterisk Cli
Database put whitelist 888888 1
Then you can use db put and db get in custom app. To send each call to proper place ( Anonymous into space ie.)
There are other solutions but question is how big is your system. And do prefer to allow most of calls and block just few or the other hand.
If you need example dial plan with db put and db get just post here. I ll post that code tommorow
Best maciej