From what I understand, it was with great horror. George V felt that the international community had failed the Romanovs. He had been unable to offer them asylum in Britain, and that had cost them their lives. Seeing the nation formerly known as Austria-Hungary transitioning into a republican government, a guilt-stricken George actively took steps to ensure that the same fate didn't befall its former kaiser, Karl the Blessed. George sent a seasoned soldier named Edward Lisle Strutt to Austria with strict instructions to ensure that the former kaiser and his family made it out of the country safely.

To be clear, it has also been claimed that George had ordered covert operations to get the Romanovs to safety, but the source isn't a scholarly one. It comes from an interview with Prince Michael of Kent (George V's grandson), who was attempting to clear his grandfather's reputation over his perceived inaction regarding the Romanovs. From what I understand, part of the difficulty of rescuing the Romanovs is that no one knew where they were being kept.

That's the short answer, and the one that's most relevant to your question. I'm going to elaborate more on the Strutt/Karl episode even though it's a digression, just in case anyone finds the anecdote as fascinating as I do.

Despite the pressure put upon him by the new republican government, Kaiser Karl of Austria had been reluctant to officially abdicate. The Habsburgs had ruled over Austria for centuries, and he still saw himself as its legitimate ruler. Although Karl was widely-loved by the general populace (he was known as the freidenkaiser [Peace Emperor] because of his attempt to sue for peace during the war), there were factions in the country who saw him as a symbol of the old order and would gladly see him put to death. The republican government gave Karl the option of abdication or imprisonment.

Recognizing that the kaiser had no intention of surrendering his claim, Strutt began to make plans for a royal train to take the royal family to exile in Switzerland. He encountered stiff resistance from Chancellor Renner of the new republican government, who refused to allow the kaiser to leave the country without first abdicating his claim to the throne. Although sympathetic to the kaiser's plight, the British government wasn't able to offer any official protection to the kaiser, and had informed Strutt that he was on his own.

So Strutt did the only thing he could. He bluffed Renner, placing a telegram on the table which stated that, should the kaiser be refused safe passage from the country, the British would re-enforce the Allied blockade, preventing all food trains from entering war-stricken Austria. It was a piece of paper with no real validity behind it, but Renner was unwilling to call Strutt's bluff. The kaiser and his family were allowed to leave Austria by train without having surrendering their claim to the throne. It was a grand departure, allowing them to leave with dignity and leaving open the possibility of a triumphant return.

Source: "A Heart for Europe: The Lives of Emperor Charles and Empress Zita of Austria", "Uncrowned Emperor: The Life and Times of Otto von Habsburg"