I had the same problem with my new iPhone X yesterday, restoring from my previous iPhone 7. never saw this message before in any previous iPhone upgrades from 5, 6. 7, or my wife’s 8, but this time the same message was repeatedly popping up about every minute, across any screen, during any task.
I BELIEVE THE PROBLEM IS BECOMING CLEARLY DEFINED AND SOLVABLE, BUT WILL NEED A SOFTWARE UPDATE FROM APPLE, AND MORE THOUGHT ABOUT HOW TO FOLLOWUP WITH THE 64BIT APP ISSUE.
My new iPhone X was still in the process of restoring images and apps after 24hours, and the pop up message was constant from yesterday afternoon. I researched a number of online resources mid afternoon with no luck (not here though) and then Verizon, which passed me to APPLE Support. Two and a half hours later, and two case numbers, the recommended APPLE solution was to force a reset to factory settings then start the transfer over again from iPhone 7 to iPhone X. I replied that I would see if the restore completed overnight and then call the APPLE STORE SUPPORT line 1-800-275-2273 back this morning, for the next steps.
After ending my phone call I began researching possible APPLE online support resources and saw that my same question had been asked and a couple of solutions offered in the follow up discussion. Since it was more then 30 hours since my upgrade had started and I had checked all my image files and apps, I followed the suggestion made below to STOP RESTORE in the iCloud BACKUP and the pop up message immediately stopped. Nothing sees to be missing from my new iPhone X files, apps, or function.
Thinking about it afterward, it seems that this issue was caused by a convergence of factors transferring from 32 to 64 bit operating systems by APPLE, but no screening tool to check existing apps in earlier iPhone versions to be sure they would transfer successfully to the iPhone X. There was no context in the pop up message to guide anyone to think about an app as the problem. APPLE should think about a software update to stop trying to restore a failed app download after a few (3?) attempts and place it in an error file for future reference. We learned this with Microsoft upgrades years ago, and now APPLE is facing a huge problem with 32 bit apps and customers wait for their iPhone X’s in the coming months. Some kind of screening app to check installed versions prior to upgrade, and sharing this problem/solution with the many APPLE and carrier tech support staff as a near term solution or alternatve may also be helpful. Perhaps APPLE could use email, txt msg, or Facebook to get a quick message out to concerned parties now and save a lot to customer and tech time on this issue.