If this is on one ticket then your bags will be checked through. You will have to go to the Delta PDC desk just after passport control.
You don't go through customs leaving countries (or common travel zones like Schengen) only when arriving.
Perhaps you are mixing customs up with immigration.
Greece to NL is like a usa domestic flight. If you have to claim your bags from transavia and check them in yourself with delta make sure you have plenty of time between flights. In terms of timing and procedure an awful lot will depend on whether this is 1 ticket with bags being transferred vs 2 separate tickets with self-transfer. I know DL and HV have codeshares to some of HV's destinations but don't know if Kreta is one of them. And I don't know the extent of interlining outside of the codeshare destinations.
KLM use Transavia as a feeder airline from destinations like this so I am 99.9% sure they will transfer bags to Delta at AMS.
You are right! I see HV on delta routes from HER thru AMS to the states on delta.com And the HV flights carry klm codeshare numbers, not DL codeshare numbers.Edited: 15 May 2018, 02:38