From the article:

“Every time we accelerated on the highway, whale juice would pour into the windows of the car, and it was the rankest thing on the planet.”

It does not sound legal.

From NOAA.gov

Can you keep a protected species part found on the beach?

In some cases, yes, you may keep the part. You may collect and keep any bones, teeth, or ivory from a non-ESA listed marine mammal found on a beach or land within one-quarter mile of an ocean, bay, or estuary. You may not collect parts from a carcass or parts with soft tissues attached.

Any marine mammal bones, teeth, or ivory that you collect must be identified and registered with the nearest NOAA Fisheries Regional Office. You may contact the appropriate Stranding Network Coordinator in your region for assistance. Marine mammal parts collected in this manner may not be bought or sold.

A dead marine mammal with soft tissue is a stranded animal and you should report it to the nearest NOAA Fisheries Stranding Network Coordinator so that the animal may be sampled for scientific research purposes and properly disposed of. You may not collect parts from a stranded animal.

Parts from ESA-listed species, including threatened or endangered species, may not be collected without a permit or other authorization.

Edit: Great job by an environmental attorney…