That's just how extradition law works: you're on loan, not given over forever, and in particular in the EU, you can't use a European Arrest Warrant just to grab

That's just how extradition law works: you're on loan, not given over forever, and in particular in the EU, you can't use a European Arrest Warrant just to grab someone so you can extradite them outside the EU without asking the origin state's permission, unless you're seriously implying he'd be black-bagged.