This visiting card is tucked into a page of a scrap book titled 'Arctic Scraps' which most probably was compiled by Lady Jane Franklin's son in law, Reverend John Philip Gell.
Sir George Back (1796-1878) accompanied Sir John Franklin on his first expedition to the Arctic in 1818 and took part in two overland expeditions with Franklin in the 1820s to chart the north Canadian coast. He made two more expeditions to the Arctic before retiring due to ill health.
When concerns were raised about Franklin's 1845 expedition to discover the North West Passage, which had not been heard from for several years, Back became a member of the Arctic Council which was formed by the Admiralty to advise on the search for the Franklin Expedition.
This visiting card was most likely left for Lady Franklin or Franklin's daughter Eleanor and her husband when Back visited them to inform her about the search.