What triggers the 'update contact details' option on calls?

When I make a call to one of my Contacts using the Phone app on iOS 17, I have started to get a request to Update their details at the top of the call screen. The suggested details are nonsense. I think my contact has managed to mess something up on their iPhone (which I think is also running iOS 17), so I'd like to know what controls the contact details that is shared when making/receiving a call with someone who has different details stored in their Contacts app, so that it would trigger this Update option to appear. I've asked my contact to check the details on their "My Card", and they say that their name information (which is what I am being prompted to Update) is what I have already. So this is making me think that it is not the My Card that is controlling this, or we need to dig in more detail. Any ideas?

Some additional context that may be helpful:

• This issue originates from my father, who called me for help a few days ago because his iPhone was stuck on a screen and he couldn't get out of it. So he'd called me on my mother's iPhone and provided the screenshot below. It looks to me like a Poster editing screen (not something I've used but I know it exists), and tapping on Cancel in the top-left was doing nothing. Given that he had just called the doctor, my theory was that he'd called using a Contact and, at the end of the call, my father went to tap on the call End button but the doctor ended the call first and instead he tapped on the "Contact Photo & Poster" option of the doctor's contact card. This would explain how he ended up in the screenshot, although not why he was unable to exit it. In the end, we just restarted his iPhone.

• The new details that I am being asked to Update when I call my father is "Doctor (day)". This cannot be a coincidence. However, as above, my father tells me that when he looks at his My Card, his name details are correct (he has not changed profession...). I also cannot explain why contact details from his doctor would have polluted his contact details.

[Re-Titled by Moderator]