score:4
First, US CBP does check warrants and second, US CBP has the authority in Canada and most likely other locales) to detain someone while they conduct an inspection.
Note that some warrants are very minor - missing payment on a traffic ticket. Some are major - skipping out on a murder trial. And there are local, state, and federal warrants. You need to have the bad fortune of either committing a serious enough local crime to be put into NCIC or a state or federal crime which are automatically sucked into the national crime database.
If you trip the warrant detection system, I’d imagine you’d be detained until the relevant authorities are contacted and they decide whether to extradite you or release you. Since extradition costs money, paperwork, and time (days), it’s more than likely that for most minor things that you’ll be put back on the flight or a later flight - where depending on the circumstances you might get re-arrested on arrival in the physical USA. Even if you have a minor warrant, I’d expect that if you’re flying back to the jurisdiction the arrest warrant was issued in, the CBP agent would give those authorities a courtesy phone call.