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I couldn't find an easy way.

I ended up using iCloud contacts on the web - export the contact, delete it, re-import it. It doesn't import the contact poster, as contacts on the web doesn't know what they are. I think you can do the same on a laptop.

One of them (it's a while since I did this!) also trashes the contact icon which I wanted to keep, so experiment with the web and MacOS version of contacts to see which works best for you.
 
Have you tried this? (this is for iPadOS 18 so button locations might differ)

  1. Open Contacts app
  2. Open your card at the top of the list
  3. Tap "Edit" in the top right corner of the screen
  4. Tap "Edit" under your image
  5. Swipe up on your image
  6. Tap the trashcan icon
 
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