Door card clamps (barnacles)

[D_SheerDrivingPleasure]

Today I removed a front door card to replace a blown speaker. When removing the door card these small metal attachment clamps came off with the door card rather than remaining attached to the door itself. This was probably because I lifted the card upwards vs pulling outward.

It's not possible to re-attached the door card properly without removing the clamps from the card and slotting these clamps into the door itself.

Any tips to remove the clamps from the door card without mangling the card or myself?