I'm wondering if perhaps you didn't drain both gray tanks? Does the shower drain work right now if you dumped a few gallons of water into it?
If it's not a full tank, rather than calling a vendor, place a bath towel on the vanity floor under the sink, then carefully remove the P-trap. It Those are large plastic hand-tightened nuts on the trap. You should be able to remove it. Then dump the trap out, outside and see if there was a chunk of construction debris in it or similar. Just a shot but worth it to check it.