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Don't associate a photo with that Contact entry? Leave that field blank.

I have some Contacts without photos. You have to add pix if you want them.
 
Google contacts will obtain a contact photo from the user if that user is also a gmail user and has added a photo. I don't think there's anything you can do about that.

Does iCloud do the same thing?
 
I haven't noticed Google doing that but I've added photos to my Contacts that are most personal to me and they would override your example.

Can't say about iCloud.
 
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