How can I clear an iPad from another company's DEP? The company I work for is in the process of enrolling all iPads into MDM and correcting devices not in the DEP.

We've found one that we've had for a while. It's in another DEP but not in another MDM... So we are prevented from adding it our DEP but we have nobody to contact about correcting it. We contacted Apple with no results. Nobody has a serialized proof of purchase, the device wasn't asset tagged properly whenever it was acquired.

My best guess was that somebody independently bought a refurb unit from a third party seller. 

How can I go about properly cataloging this into our DEP?
The organization that owns the device is normally the only entity that can release it. You can watch the traffic without impacting it but not really get around the enrollment process without a solid jailbreak and some network skills. 


Can iPad SSL/TLS traffic be inspected during DEP enrollment?


I would start with network packet capture / tracing to confirm which entity has convinced Apple to exert DEP control by logging DNS lookups or packet capture and not even pester Apple if you can't document your request in specific detail. 

If there is a clear mistake, the other third party will they will likely want to help you out or at least learn more about this hardware. 


you either will be reporting a stolen device to them or they will learn they messed up releasing that device. 
It’s also remotely possible there was a serial number mixup and they can contact Apple with you to fix that. 


Some day they could need someone else’s help and they wouldn’t want to manage your machine or be liable for infringing on your rights if they know hey are improperly managing someone else’s hardware. It's just the right thing to do if you ended up with someone else's registration in your console.

Next, if you really had to you would work with Apple and be clearer and more thorough and patient than the first time you asked for help. You will be seen as potentially someone looking to steal someone else’s hardware since Apple goes to pretty long lengths to validate a company before they allow DEP and the odds of mistakes that can’t be caught are low. 

Worst thing - even if you accomplish your goal, I doubt you will ever be able to DEP that serial that was enrolled once and released. I’ve never heard of an exception to this. Maybe Apple would budge, but the warnings the releasing company sees before they release are quite dire and clear there is no going back once they rescind your/their one time DEP enrollment of a serialized product Apple sold to a validated business account. 

You are likely going to have a long, hard  and unproductive experience with either a third party or Apple without specific documented proof a mistake was made. You might get what you want, but the desk is stacked against you accomplishing this for some really well considered reasons.