Update 25 07 2022 thank you Paul Lorenz Eichmüller for flagging and discussing the eventual Austrian SC decision: ordre public was not infringed. On the facts at issue, definitely established (though potentially wrongly, as Paul notes) by the Austrian lower courts, there had been a possibility for substantive review of the Jordanian judgment in the UK courts. Austrian ordre public could not qualify.
I reviewed Pikamae AG’s Opinion in C-568/20 J v H Limited here. The issue is whether, exequatur having been abandoned in Brussels Ia, arguments as to whether the a judgment issued in a third, non EU Member, State of origin be at all covered by Brussels Ia may be raised by way of an Article 45 objection to recognition and enforcement.
The CJEU has now held and first of all clarifies its findings in C-129/92 Owens Bank. : Owens Bank does not mean that a decision adopted on the basis of a judgment emanating from a third State, in accordance with the rules on jurisdiction and procedure of a Member State, may never fall within the scope of that regulation.  it is sufficient (but also necessary, GAVC) that they be judicial decisions which, before their recognition and enforcement are sought in a State other than the State of origin, have been, or have been capable of being, the subject, in that State of origin and under various procedures, of an inquiry in adversarial proceedings. This re-emphasises the audi alteram partem principle such as emphasised eg in CJEU Zulikarpašić. It also means that ‘exequatur sur exequatur ne vaut‘ is not quite dead, as has been suggested – a mere confirmative order of an ex-EU judgment without adversarial proceedings would not enjoy free movement.
At  the Court moreover instructs, with reference to the principle of mutual trust, that the courts in the State of recognition, must not apply the definition restrictively. In the case at issue  the High Court order at issue in the main proceedings was, at the very least, the subject of a summary hearing in the Member State of origin, hence it qualifies as a ‘judgment’.
While the Court effectively acknowledges that this amounts to Brussels Ia-sanctioned recognition and enforcement of non-EU judgments through the backdoor (‘on the substance, that [UK, GAVC] order was made so as to give effect to judgments delivered in a third State which are not, as such, enforceable in the Member States’: ), A45’s grounds of refusal, including infringement of ordre public, remain available: 
Such an infringement may, inter alia, lie in the fact that the party against whom enforcement is sought was not able to defend him or herself effectively before the court of origin and to challenge the decision sought to be enforced in the Member State of origin
EU Private International Law, 3rd ed 2021, 2.573.
2 Replies to “J v H Limited. CJEU holds third country judgments may, under circumstances, be smuggled into Brussels Ia via the backdoor. Yet they will be vulnerable to ordre public exceptions.”