Thanks very!
This problem has been ongoing ever since Apple Pay was introduced, so I had already restarted the iPhone, and I had removed and added back the credit cards in Apple Pay along the way.
I most certainly have the "Allow websites to check for Apple Pay" enabled in Preferences.
What I haven't done is to delete the .plist. I just checked that, and I found not one, but TWO com.apple.safari.plist files differing in the alphanumeric characters that were appended to the the ".plist" extension. I deleted both. NOW, I have to find a site that offers Apple Pay to test this.
Interestingly, I've had an ongong problem with Finder in which, after the machine has been booted for a while, there will be 2 or 3 Finder windows open, but I can launch none of them by clicking on Dock's Finder icon or even by right-clicking that icon and selecting one. The solution to that very old prolblem came when I discovered that there were THREE .plist files for Finder. That was the ONLY problem with Finder, and deleting the preference list files cured it. I'm therefore optimistic about your suggestion working for this Apple Pay problem. I'll post a follow-up when I get a chance to check it out.